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Theorem hbaltg 25466
Description: A more general and closed form of hbal 1753. (Contributed by Scott Fenton, 13-Dec-2010.)
Assertion
Ref Expression
hbaltg  |-  ( A. x ( ph  ->  A. y ps )  -> 
( A. x ph  ->  A. y A. x ps ) )

Proof of Theorem hbaltg
StepHypRef Expression
1 alim 1568 . 2  |-  ( A. x ( ph  ->  A. y ps )  -> 
( A. x ph  ->  A. x A. y ps ) )
2 ax-7 1751 . 2  |-  ( A. x A. y ps  ->  A. y A. x ps )
31, 2syl6 32 1  |-  ( A. x ( ph  ->  A. y ps )  -> 
( A. x ph  ->  A. y A. x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1550
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-5 1567  ax-7 1751
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