Theorem al2im 1742

Description: Closed form of al2imi 1743. Version of alim 1738 for a nested implication. (Contributed by Alan Sare, 31-Dec-2011.)

Assertion

Ref	Expression
al2im	|- ( A. x ( ph -> ( ps -> ch ) ) -> ( A. x ph -> ( A. x ps -> A. x ch ) ) )

Proof of Theorem al2im

Step	Hyp	Ref	Expression
1		alim 1738	. 2 |- ( A. x ( ph -> ( ps -> ch ) ) -> ( A. x ph -> A. x ( ps -> ch ) ) )
2		alim 1738	. 2 |- ( A. x ( ps -> ch ) -> ( A. x ps -> A. x ch ) )
3	1, 2	syl6 35	1 |- ( A. x ( ph -> ( ps -> ch ) ) -> ( A. x ph -> ( A. x ps -> 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:  al2imi  1743  bj-alanim  32596  al3im  37938  19.41rgVD  39138