Theorem mp3an1i 1184

Description: An inference based on modus ponens.

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 14	. . 3 |- ((ps /\ ch /\ th) -> (ph -> ta))
4	1, 3	mp3an1 1178	. 2 |- ((ch /\ th) -> (ph -> ta))
5	4	com12 14	1 |- (ph -> ((ch /\ th) -> ta))

Syntax hints:   -> wi 3   /\ wa 240   /\ w3a 858

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 164  df-an 242  df-3an 860

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