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Theorem bj-hbalt 13054
Description: Closed form of hbal 1453 (copied from set.mm). (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-hbalt  |-  ( A. y ( ph  ->  A. x ph )  -> 
( A. y ph  ->  A. x A. y ph ) )

Proof of Theorem bj-hbalt
StepHypRef Expression
1 alim 1433 . 2  |-  ( A. y ( ph  ->  A. x ph )  -> 
( A. y ph  ->  A. y A. x ph ) )
2 ax-7 1424 . 2  |-  ( A. y A. x ph  ->  A. x A. y ph )
31, 2syl6 33 1  |-  ( A. y ( ph  ->  A. x ph )  -> 
( A. y ph  ->  A. x A. y ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1329
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-5 1423  ax-7 1424
This theorem is referenced by:  bj-nfalt  13055
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