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Theorem bj-hbalt 30804
Description: Closed form of hbal 1868. When in main part, prove hbal 1868 and hbald 1872 from it. (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 1653 . 2  |-  ( A. y ( ph  ->  A. x ph )  -> 
( A. y ph  ->  A. y A. x ph ) )
2 ax-11 1866 . 2  |-  ( A. y A. x ph  ->  A. x A. y ph )
31, 2syl6 31 1  |-  ( A. y ( ph  ->  A. x ph )  -> 
( A. y ph  ->  A. x A. y ph ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1403
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-4 1652  ax-11 1866
This theorem is referenced by:  bj-hbext  30828  bj-nfalt  30829  bj-cbv3ta  30834
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