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Theorem hbalg 36786
Description: Closed form of hbal 1895. Derived from hbalgVD 37169. (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 1680 . . 3  |-  ( A. y ( ph  ->  A. x ph )  -> 
( A. y ph  ->  A. y A. x ph ) )
2 ax-11 1893 . . 3  |-  ( A. y A. x ph  ->  A. x A. y ph )
31, 2syl6 35 . 2  |-  ( A. y ( ph  ->  A. x ph )  -> 
( A. y ph  ->  A. x A. y ph ) )
43axc4i 1954 1  |-  ( A. y ( ph  ->  A. x ph )  ->  A. y ( A. y ph  ->  A. x A. y ph ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1436
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-10 1888  ax-11 1893  ax-12 1906
This theorem depends on definitions:  df-bi 189  df-ex 1661  df-nf 1665
This theorem is referenced by:  hbexgVD  37170
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