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Theorem a7s 1709
Description: Swap quantifiers in an antecedent. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
a7s.1  |-  ( A. x A. y ph  ->  ps )
Assertion
Ref Expression
a7s  |-  ( A. y A. x ph  ->  ps )

Proof of Theorem a7s
StepHypRef Expression
1 ax-7 1708 . 2  |-  ( A. y A. x ph  ->  A. x A. y ph )
2 a7s.1 . 2  |-  ( A. x A. y ph  ->  ps )
31, 2syl 15 1  |-  ( A. y A. x ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527
This theorem is referenced by:  cbv3hv  1737  cbv1h  1918  cbv2h  1920  sb9i  2034  ax10-16  2129  ax10ext  27606  ax9lem13  29152
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8  ax-7 1708
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