Theorem bj-hbalt 12552

Description: Closed form of hbal 1421 (copied from set.mm). (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 1401	. 2 |- ( A. y ( ph -> A. x ph ) -> ( A. y ph -> A. y A. x ph ) )
2		ax-7 1392	. 2 |- ( A. y A. x ph -> A. x A. y ph )
3	1, 2	syl6 33	1 |- ( A. y ( ph -> A. x ph ) -> ( A. y ph -> A. x A. y ph ) )

Syntax hints:   -> wi 4   A.wal 1297

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-5 1391  ax-7 1392

This theorem is referenced by:  bj-nfalt  12553