By Michael Hurley, CBS Boston

BOSTON (CBS) — On the final day of amicus briefs being allowed to be filed with the U.S. Court of Appeals for the Second Circuit in the case of Tom Brady vs. the NFL, the Patriots quarterback got some support from the largest federation of unions in the United States.

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The AFL-CIO — The American Federation of Labor and Congress of Industrial Organizations — filed an amicus brief with the Second Circuit on Tuesday, referring to NFL commissioner Roger Goodell’s actions as arbitrator as “error” and requesting that the award be vacated.

“Because the Commissioner — who issued the discipline to Brady in the first instance — failed to follow basic procedural fairness and acted arbitrarily as an employer seeking to justify his own disciplinary decision rather than as a neutral arbitrator considering an appeal — his decision should be vacated,” the brief, prepared by attorney James Coppess, stated.

The brief brings to light the issue of fundamental fairness, namely whether Goodell could have been impartial as arbitrator when he was ruling on his own decision and relying on an investigation which he commissioned. The request for filing noted that the Second Circuit judges gave Goodell the level of deference “ordinarily extended to decisions of neutral arbitrators.” However, “the lack of procedural fairness in the underlying decision” proved Goodell to not be a neutral party to the proceedings, according to the filing.

READ: AFL-CIO’s Amicus Brief Supporting Tom Brady

“While the NFL and NFLPA bargained to allow the Commissioner to hear appeals of disciplinary decisions, they did not agree to let the Commissioner, sitting as an appellate arbitrator, to act in a manner that is arbitrary and capricious,” the brief stated. “Regardless of who hears appeals, labor arbitration always must be fundamentally fair.”

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The brief echoed Olson’s argument that the accusations and grounds for punishment cannot change during the appeals process, as they did for Brady. Originally charging with being “generally aware” of football deflation, Goodell upped the charges to knowing about, approving of, consenting to and providing inducements and rewards in support of a scheme.

“The substantiality of ‘the Commissioner’s shifting rationale for Brady’s discipline,’ serves as strong evidence that the Commissioner was not acting as a neutral arbitrator considering an appeal at all, but rather as an employer seeking to justify his own initial disciplinary decision,” the brief concluded.

While the NFLPA is included in the AFL-CIO’s affiliated unions, the AFL-CIO’s involvement with the case lends credence to attorney Ted Olson’s claim that the Second Circuit’s decision affects not just football players, but all employees who are subject to collective bargaining agreements.

“… [T]he AFL-CIO has extensive experience with the operation of arbitration procedures in the disciplinary setting and a significant interest in the application of the proper standard for judicial review of decisions rendered pursuant to arbitration procedures,” the brief stated.

The brief is the third filed with the court in support of Brady, with the first coming from 21 scientists from around the country, and the other coming from the New England Patriots. Attorney Kenneth Feinberg also filed an amicus brief on Tuesday, likewise bringing into question the lack of fundamental fairness in the arbitration proceedings. The briefs were written in support of Brady, who (by way of Olson) formally requested a rehearing from the Second Circuit after losing a 2-1 panel decision that reinstated the four-game suspension placed upon him by Goodell.

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The Second Circuit is expected to decide on whether to rehear the case — an extremely rare occurrence — by the end of June. The presence of an organization as powerful as the AFL-CIO, as well as the experience of Olson, figure to at least give Brady a chance at achieving that goal.