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Theorem alcoms 2162
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-11 2161 . 2 (∀𝑦𝑥𝜑 → ∀𝑥𝑦𝜑)
2 alcoms.1 . 2 (∀𝑥𝑦𝜑𝜓)
31, 2syl 17 1 (∀𝑦𝑥𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1536
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-11 2161
This theorem is referenced by:  cbv2h  2427  mo3  2647  bj-nfalt  34119  bj-cbv3ta  34184  bj-cbv2hv  34195  wl-equsal1i  34906  wl-mo3t  34935  axc11n-16  36192  axc11next  41044
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