Theorem mp3an3an 1430

Description: mp3an 1424 with antecedents in standard conjunction form and with two hypotheses which are implications. (Contributed by Alan Sare, 28-Aug-2016.)

Hypotheses

Ref	Expression
mp3an3an.1	|- ph
mp3an3an.2	|- ( ps -> ch )
mp3an3an.3	|- ( th -> ta )
mp3an3an.4	|- ( ( ph /\ ch /\ ta ) -> et )

Assertion

Ref	Expression
mp3an3an	|- ( ( ps /\ th ) -> et )

Proof of Theorem mp3an3an

Step	Hyp	Ref	Expression
1		mp3an3an.2	. 2 |- ( ps -> ch )
2		mp3an3an.3	. 2 |- ( th -> ta )
3		mp3an3an.1	. . 3 |- ph
4		mp3an3an.4	. . 3 |- ( ( ph /\ ch /\ ta ) -> et )
5	3, 4	mp3an1 1411	. 2 |- ( ( ch /\ ta ) -> et )
6	1, 2, 5	syl2an 494	1 |- ( ( ps /\ th ) -> et )

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:  mp3an2ani  1431  nn0p1elfzo  12510  ftc1anclem6  33490