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Theorem alcoms 1897
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 1896 . 2  |-  ( A. y A. x ph  ->  A. x A. y ph )
2 alcoms.1 . 2  |-  ( A. x A. y ph  ->  ps )
31, 2syl 17 1  |-  ( A. y A. x ph  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1435
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-11 1896
This theorem is referenced by:  cbv3hv  2016  cbv2h  2077  mo3  2306  bj-nfalt  31265  bj-cbv3ta  31270  bj-cbv2hv  31294  bj-mo3OLD  31417  wl-equsal1i  31840  wl-mo3t  31869  axc11n-16  32478  axc11next  36727
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