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

Step	Hyp	Ref	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 )
3	1, 2	syl6 35	. 2 |- ( A. y ( ph -> A. x ph ) -> ( A. y ph -> A. x A. y ph ) )
4	3	axc4i 1954	1 |- ( A. y ( ph -> A. x ph ) -> A. y ( A. y ph -> A. x A. y ph ) )

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