Horton Automatics (“Horton”) sued The Industrial Division of the Communication Workers of America, AFL-CIO, and Local 86122 (“the union”), seeking to vacate an arbitration award. The district court granted summary judgment to Horton, vacating the affirmative relief granted by the award. The union appeals, and we affirm.

I.

Horton and the union were parties to a collective bargaining agreement (“CBA”), Article 13 of which provided for arbitration of grievances concerning discipline but limited the arbitrator’s role:

In determining whether the Company had cause to impose the aggrieved disciplinary action, the Arbitrator shall be limited to deciding whether a published rule or regulation which formed the basis for the discipline was in fact reasonable and violated by the employee.... [A]ny departure or deviation by the arbitrator from the expressed terms, or requirements, set forth in this Article shall render the Arbitrators award null and void and of no effect.

The CBA granted Horton the exclusive right to “discharge employees for just cause, subject to contractual provisions,” and removed seniority from any employee “discharged for just cause subject to contractual provisions.”

*255 Ruben de la Garza, a Horton employee, operated a tapper, an electric drill that scores threads into holes so that a bolt can later be fitted into the threaded hole. Horton equipped the tapper with an adjustable guard, which employees were required to have in place whenever the tapper was turned on. The tapper had to be lubricated frequently either by using a spray bottle or by holding a small container of lubricant under the tap so that the tap was submerged. The latter method required the tapper to be turned off, because the operator had to reach past the safety guard to put a hand near the tap.

In 2010, Horton’s facilities maintenance manager asked de la Garza to demonstrate how the tapper operated. De la Garza secured a piece of metal in the machine’s vice, reached past the guard, held a small cup of lubricant under the tap, and turned on the machine. During a subsequent investigation, de la Garza admitted that he had operated the tapper in that manner for about eighteen months.

For most work-rule violations, Horton had established a five-step process, beginning with a documented reminder and culminating in an investigatory suspension that could lead to termination. For more serious violations, such as a “[s]afety violation that causes serious injury or could have caused serious injury,” Horton could skip the warning steps. Horton determined that de la Garza’s repeated unsafe operation of the tapper was a serious violation, so it decided to skip a step, as it did whenever an employee tampered with or bypassed a safety guard. Because de la Garza was already at step three, Horton skipped a final written warning and discharged him.

The union appealed the discharge to arbitration, and the parties agreed to frame the issue as whether “the Employer ha[d] just cause to discharge Ruben DeLaGarza ... in accordance with the provisions of the [CBA]? If not, what is the appropriate remedy?” The arbitrator found that the “serious injury” safety rule was reasonable and that de la Garza had violated the rule.

Nonetheless, the arbitrator found “that a question exists as to whether or not [Horton] is applying discipline consistently to similarly situated employees.” Although he acknowledged that Horton had consistently skipped a warning step for guard violations, he noted that Horton did not always skip a step for other serious safety violations. Because he was “not totally convinced” that Horton should treat guard violations more seriously than other violations, he found that Horton did not have just cause to terminate de la Garza, whom he reinstated.

Horton asked the district court to vacate the arbitration award, arguing that the arbitrator had exceeded his power as defined in the CBA. The Union argued that the arbitrator was entrusted with interpreting the entire CBA, including “aspirational goals of harmonious relations between the company and its employees” and the “just cause” references. The court granted Horton’s motion for summary judgment and denied the Union’s motion because of the “plain and unambiguous import” of the limitations contained in Article 13 of the CBA. The court vacated “any affirmative relief awarded” to de la Garza in the arbitration award.

II.

In a suit to vacate an arbitration award, we review a summary judgment de novo. Weber Aircraft Inc. v. Gen. Warehousemen & Helpers Union Local 767, 253 F.3d 821, 824 (5th Cir. 2001). Judicial review of arbitration awards is “extremely limited,” but judicial deference ends “where the ar *256 bitrator exceeds the express limitations of his contractual mandate.” 1

III.

A.

“Arbitration is a matter of contract.” Rain CII Carbon, LLC v. ConocoPhillips Co., 674 F.3d 469, 472 (5th Cir. 2012). If a contract sets forth a “limitation on the authority of an arbitrator, we will vacate an award that ignores the limitation.” Apache Bohai Corp. LDC v. Texaco China BV, 480 F.3d 397, 401 (5th Cir. 2007). “[Limitations must be plain and unambiguous and ... we resolve all doubts in favor of arbitration.” Id. at 404.

The language of the CBA is plain and unambiguous. To determine whether Horton had cause to discharge de la Garza, the arbitrator was expressly limited to answering two questions: (1) whether the serious-injury rule was reasonable and (2) whether de la Garza violated the rule. Having answered both questions in the affirmative, the arbitrator was bound by the CBA to decide that Horton had cause. In asking and answering a third question — whether Horton had applied discipline consistently in similar situations — the arbitrator exceeded his authority under the CBA.

The union does not argue that Article 13 allows an arbitrator, in deciding whether Horton had cause, to consider more than whether the employee had violated a reasonable rule. Instead, the union maintains that Article 13’s “cause” is meaningfully distinct from “just cause,” used elsewhere in the CBA and not defined. The union contends that an arbitrator could rationally conclude that cause and just cause are not the same thing and that some meaning should be given to just cause beyond the two questions of Article 13.

Furthermore, the union contends, the issue actually submitted by the parties gave the arbitrator broad authority to determine just cause as defined by the CBA as a whole, not just by Article 13. The union notes that an arbitrator’s authority is granted both by the parties’ agreement to arbitrate and by their submission agreement. 2

The problem with the union’s position is that cause and just cause are synonymous in the context of labor arbitration, despite the latter’s modifier. 3 In Container Products, Inc. v. United Steelworkers of America, 873 F.2d 818, 818-20 (5th Cir. 1989), for example, the contract required a showing of “proper cause,” the parties submitted the issue of whether the company had “just cause,” and the arbitrator found evidence of “cause” and implicitly of “just cause.” This court treated all three terms interchangeably and held that an implicit finding of “just cause” bound the arbitrator under the contract. Id. at 820.

There is no discrepancy, therefore, between Article 13’s cause and just cause, as used elsewhere in the CBA. The arbitra *257 tor was not granted authority by the modifier “just” to consider a broad range of issues. Similarly, the submitted issue referred to just cause “in accordance with the provisions of the [CBA].” Just cause was not defined in the CBA, but its synonym, cause, was — in Article 13. Neither the CBA nor the submitted issue granted the arbitrator authority to answer any question beyond the express limitations contained in Article 13. The arbitrator’s decision to ask and answer an additional question, therefore, exceeded his authority under the CBA and must be vacated.

B.

The Union asserts that we ought to remand to the arbitrator for further proceedings, should we decide to vacate the award. We disagree.

In certain instances, remand for further arbitration proceedings is appropriate, and this court “must not foreclose further proceedings by settling the merits according to [our] own judgment of the appropriate result, since this step would improperly substitute a judicial determination for the arbitrator’s decision that the parties bargained for in the [CBA].” United Paperworkers Int’l Union, AFL-CIO v. Misco, Inc., 484 U.S. 29, 40 n. 10, 108 S.Ct. 364, 98 L.Ed.2d 286 (1987). In this case, however, the merits have already been decided, implicitly, by the arbitrator himself.

Article 13 of the CBA prescribes that the arbitrator must determine whether Horton had cause by deciding whether the rule in question was reasonable and was actually violated by the disciplined employee. The arbitrator has already found that Horton’s serious-injury rule was reasonable and that de la Garza actually violated it. Because the CBA defines cause to exist where those questions are answered affirmatively, and the arbitrator answered them affirmatively, the arbitrator, implicitly, found that Horton had cause to discharge de la Garza. 4 Under the CBA — which limits the arbitrator to deciding whether Horton had cause — and under the submitted issue — which asked the arbitrator to determine a proper remedy only if Horton lacked just cause — the arbitrator has nothing more to do. There is therefore no reason to remand.

The judgment, which vacates the arbitrator’s award with respect to any affirmative relief to the union, is AFFIRMED.