Theorem al3im 37938

Description: Version of ax-4 1737 for a nested implication. (Contributed by RP, 13-Apr-2020.)

Assertion

Ref	Expression
al3im	|- ( A. x ( ph -> ( ps -> ( ch -> th ) ) ) -> ( A. x ph -> ( A. x ps -> ( A. x ch -> A. x th ) ) ) )

Proof of Theorem al3im

Step	Hyp	Ref	Expression
1		alim 1738	. 2 |- ( A. x ( ph -> ( ps -> ( ch -> th ) ) ) -> ( A. x ph -> A. x ( ps -> ( ch -> th ) ) ) )
2		al2im 1742	. 2 |- ( A. x ( ps -> ( ch -> th ) ) -> ( A. x ps -> ( A. x ch -> A. x th ) ) )
3	1, 2	syl6 35	1 |- ( A. x ( ph -> ( ps -> ( ch -> th ) ) ) -> ( A. x ph -> ( A. x ps -> ( A. x ch -> A. x th ) ) ) )

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: (None)