Theorem hbalg 36365

Description: Closed form of hbal 1870. Derived from hbalgVD 36749. (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 1655	. . 3 |- ( A. y ( ph -> A. x ph ) -> ( A. y ph -> A. y A. x ph ) )
2		ax-11 1868	. . 3 |- ( A. y A. x ph -> A. x A. y ph )
3	1, 2	syl6 33	. 2 |- ( A. y ( ph -> A. x ph ) -> ( A. y ph -> A. x A. y ph ) )
4	3	axc4i 1928	1 |- ( A. y ( ph -> A. x ph ) -> A. y ( A. y ph -> A. x A. y ph ) )

Syntax hints:   -> wi 4   A.wal 1405

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1641  ax-4 1654  ax-5 1727  ax-6 1773  ax-7 1816  ax-10 1863  ax-11 1868  ax-12 1880

This theorem depends on definitions:  df-bi 187  df-ex 1636  df-nf 1640

This theorem is referenced by:  hbexgVD  36750