Theorem bj-hbalt 32671

Description: Closed form of hbal 2036. When in main part, prove hbal 2036 and hbald 2041 from it. (Contributed by BJ, 2-May-2019.)

Assertion

Ref	Expression
bj-hbalt	|- ( A. y ( ph -> A. x ph ) -> ( A. y ph -> A. x A. y ph ) )

Proof of Theorem bj-hbalt

Step	Hyp	Ref	Expression
1		alim 1738	. 2 |- ( A. y ( ph -> A. x ph ) -> ( A. y ph -> A. y A. x ph ) )
2		ax-11 2034	. 2 |- ( A. y A. x ph -> A. x A. y ph )
3	1, 2	syl6 35	1 |- ( A. y ( ph -> A. x ph ) -> ( 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-4 1737  ax-11 2034

This theorem is referenced by:  bj-hbext  32701  bj-nfalt  32702  bj-cbv3ta  32710