Theorem mp3anl1 1321

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 114	. . 3 |- ( ( ph /\ ps /\ ch ) -> ( th -> ta ) )
4	1, 3	mp3an1 1314	. 2 |- ( ( ps /\ ch ) -> ( th -> ta ) )
5	4	imp 123	1 |- ( ( ( ps /\ ch ) /\ th ) -> ta )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 968

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 970

This theorem is referenced by:  mp3anr1  1324  archnqq  7358  facavg  10659  iddvds  11744