Theorem mp3an1i 1417

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 32	. . 3 |- ( ( ps /\ ch /\ th ) -> ( ph -> ta ) )
4	1, 3	mp3an1 1411	. 2 |- ( ( ch /\ th ) -> ( ph -> ta ) )
5	4	com12 32	1 |- ( ph -> ( ( ch /\ th ) -> ta ) )

Syntax hints:   -> wi 4   /\ wa 384   /\ w3a 1037

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 197  df-an 386  df-3an 1039

This theorem is referenced by: (None)