Theorem mpan2i 431

Description: An inference based on modus ponens. (Contributed by NM, 10-Apr-1994.) (Proof shortened by Wolf Lammen, 19-Nov-2012.)

Hypotheses

Ref	Expression
mpan2i.1	|- ch
mpan2i.2	|- ( ph -> ( ( ps /\ ch ) -> th ) )

Assertion

Ref	Expression
mpan2i	|- ( ph -> ( ps -> th ) )

Proof of Theorem mpan2i

Step	Hyp	Ref	Expression
1		mpan2i.1	. . 3 |- ch
2	1	a1i 9	. 2 |- ( ph -> ch )
3		mpan2i.2	. 2 |- ( ph -> ( ( ps /\ ch ) -> th ) )
4	2, 3	mpan2d 428	1 |- ( ph -> ( ps -> th ) )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108

This theorem is referenced by:  sincosq1lem  15061