Theorem mp3an1i 1270

Description: An inference based on modus ponens. (Contributed by NM, 5-Jul-2005.)

Hypotheses

Ref	Expression
mp3an1i.1	|- ps
mp3an1i.2	|- (ph -> ((ps /\ ch /\ th) -> ta))

Assertion

Ref	Expression
mp3an1i	|- (ph -> ((ch /\ th) -> ta))

Proof of Theorem mp3an1i

Step	Hyp	Ref	Expression
1		mp3an1i.1	. . 3 |- ps
2		mp3an1i.2	. . . 4 |- (ph -> ((ps /\ ch /\ th) -> ta))
3	2	com12 27	. . 3 |- ((ps /\ ch /\ th) -> (ph -> ta))
4	1, 3	mp3an1 1264	. 2 |- ((ch /\ th) -> (ph -> ta))
5	4	com12 27	1 |- (ph -> ((ch /\ th) -> ta))

Syntax hints:   -> wi 4   /\ wa 358   /\ w3a 934

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936

This theorem is referenced by: (None)