Theorem sylgt 1749

Description: Closed form of sylg 1750. (Contributed by BJ, 2-May-2019.)

Assertion

Ref	Expression
sylgt	|- ( A. x ( ps -> ch ) -> ( ( ph -> A. x ps ) -> ( ph -> A. x ch ) ) )

Proof of Theorem sylgt

Step	Hyp	Ref	Expression
1		alim 1738	. 2 |- ( A. x ( ps -> ch ) -> ( A. x ps -> A. x ch ) )
2	1	imim2d 57	1 |- ( A. x ( ps -> ch ) -> ( ( ph -> A. x ps ) -> ( ph -> A. x ch ) ) )

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

This theorem is referenced by:  bj-sylgt2  32601  bj-nexdh  32606  bj-alrim  32683  bj-cbv3ta  32710