Theorem mp3anl1 1331

Description: An inference based on modus ponens. (Contributed by NM, 24-Feb-2005.)

Hypotheses

Ref	Expression
mp3anl1.1	|- ph
mp3anl1.2	|- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ta )

Assertion

Ref	Expression
mp3anl1	|- ( ( ( ps /\ ch ) /\ th ) -> ta )

Proof of Theorem mp3anl1

Step	Hyp	Ref	Expression
1		mp3anl1.1	. . 3 |- ph
2		mp3anl1.2	. . . 4 |- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ta )
3	2	ex 115	. . 3 |- ( ( ph /\ ps /\ ch ) -> ( th -> ta ) )
4	1, 3	mp3an1 1324	. 2 |- ( ( ps /\ ch ) -> ( th -> ta ) )
5	4	imp 124	1 |- ( ( ( ps /\ ch ) /\ th ) -> ta )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 978

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 980

This theorem is referenced by:  mp3anr1  1334  archnqq  7419  facavg  10729  iddvds  11814