Theorem mp3an1 1264

Description: An inference based on modus ponens. (Contributed by NM, 21-Nov-1994.)

Hypotheses

Ref	Expression
mp3an1.1	|- ph
mp3an1.2	|- ((ph /\ ps /\ ch) -> th)

Assertion

Ref	Expression
mp3an1	|- ((ps /\ ch) -> th)

Proof of Theorem mp3an1

Step	Hyp	Ref	Expression
1		mp3an1.1	. 2 |- ph
2		mp3an1.2	. . 3 |- ((ph /\ ps /\ ch) -> th)
3	2	3expb 1152	. 2 |- ((ph /\ (ps /\ ch)) -> th)
4	1, 3	mpan 651	1 |- ((ps /\ ch) -> th)

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

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

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

This theorem is referenced by:  mp3an12  1267  mp3an1i  1270  mp3anl1  1271  mp3an  1277  opkelcokg  4261  opkelimagekg  4271  ltfintri  4466  vfinspnn  4541  vfinspclt  4552  spaccl  6286  spacind  6287  nchoicelem3  6291  nchoicelem4  6292  nchoicelem6  6294  nchoicelem9  6297  nchoicelem12  6300  nchoicelem14  6302  nchoicelem17  6305