Theorem hbalg 38771

Description: Closed form of hbal 2036. Derived from hbalgVD 39141. (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 1738	. . 3 |- ( A. y ( ph -> A. x ph ) -> ( A. y ph -> A. y A. x ph ) )
2		ax-11 2034	. . 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 2131	1 |- ( A. y ( ph -> A. x ph ) -> A. y ( A. y ph -> A. x A. y ph ) )

Syntax hints:   -> wi 4   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-11 2034  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1705  df-nf 1710

This theorem is referenced by:  hbexgVD  39142