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Theorem alcoms 1406
Description: Swap quantifiers in an antecedent. (Contributed by NM, 11-May-1993.)
Hypothesis
Ref Expression
alcoms.1  |-  ( A. x A. y ph  ->  ps )
Assertion
Ref Expression
alcoms  |-  ( A. y A. x ph  ->  ps )

Proof of Theorem alcoms
StepHypRef Expression
1 ax-7 1378 . 2  |-  ( A. y A. x ph  ->  A. x A. y ph )
2 alcoms.1 . 2  |-  ( A. x A. y ph  ->  ps )
31, 2syl 14 1  |-  ( A. y A. x ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1283
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-7 1378
This theorem is referenced by:  bj-nfalt  10726  strcollnft  10937
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