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Theorem hbalg 28321
Description: Closed form of hbal 1710. Derived from hbalgVD 28681. (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 1545 . . 3  |-  ( A. y ( ph  ->  A. x ph )  -> 
( A. y ph  ->  A. y A. x ph ) )
2 ax-7 1708 . . 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 1758 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 1527
This theorem is referenced by:  hbexgVD  28682
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-nf 1532
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