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Theorem hbalg 28620
Description: Closed form of hbal 1722. Derived from hbalgVD 28997. (Contributed by Alan Sare, 8-Feb-2014.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
hbalg  |-  ( A. y ( ph  ->  A. x ph )  ->  A. y ( A. y ph  ->  A. x A. y ph ) )

Proof of Theorem hbalg
StepHypRef Expression
1 alim 1548 . . 3  |-  ( A. y ( ph  ->  A. x ph )  -> 
( A. y ph  ->  A. y A. x ph ) )
2 ax-7 1720 . . 3  |-  ( A. y A. x ph  ->  A. x A. y ph )
31, 2syl6 29 . 2  |-  ( A. y ( ph  ->  A. x ph )  -> 
( A. y ph  ->  A. x A. y ph ) )
43a5i 1770 1  |-  ( A. y ( ph  ->  A. x ph )  ->  A. y ( A. y ph  ->  A. x A. y ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1530
This theorem is referenced by:  hbexgVD  28998
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-nf 1535
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