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Theorem alcoms 1861
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-11 1860 . 2  |-  ( A. y A. x ph  ->  A. x A. y ph )
2 alcoms.1 . 2  |-  ( A. x A. y ph  ->  ps )
31, 2syl 16 1  |-  ( A. y A. x ph  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1397
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-11 1860
This theorem is referenced by:  cbv3hv  1978  cbv2h  2040  mo3  2272  mo3OLD  2273  wl-equsal1i  30201  wl-mo3t  30226  axc11next  31521  bj-nfalt  34651  bj-cbv3ta  34656  bj-cbv2hv  34680  axc11n-16  35120
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