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Theorem alcoms 1456
Description: Swap quantifiers in an antecedent. (Contributed by NM, 11-May-1993.)
Hypothesis
Ref Expression
alcoms.1 (∀𝑥𝑦𝜑𝜓)
Assertion
Ref Expression
alcoms (∀𝑦𝑥𝜑𝜓)

Proof of Theorem alcoms
StepHypRef Expression
1 ax-7 1428 . 2 (∀𝑦𝑥𝜑 → ∀𝑥𝑦𝜑)
2 alcoms.1 . 2 (∀𝑥𝑦𝜑𝜓)
31, 2syl 14 1 (∀𝑦𝑥𝜑𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1333
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-7 1428
This theorem is referenced by:  bj-nfalt  13409
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