Theorem hbalg 36922

Description: Closed form of hbal 1922. Derived from hbalgVD 37302. (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 1683	. . 3 |- ( A. y ( ph -> A. x ph ) -> ( A. y ph -> A. y A. x ph ) )
2		ax-11 1920	. . 3 |- ( A. y A. x ph -> A. x A. y ph )
3	1, 2	syl6 34	. 2 |- ( A. y ( ph -> A. x ph ) -> ( A. y ph -> A. x A. y ph ) )
4	3	axc4i 1980	1 |- ( A. y ( ph -> A. x ph ) -> A. y ( A. y ph -> A. x A. y ph ) )

Syntax hints:   -> wi 4   A.wal 1442

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933

This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1664  df-nf 1668

This theorem is referenced by:  hbexgVD  37303