Theorem mp3an2i 1273

Description: mp3an 1268 with antecedents in standard conjunction form and with two hypotheses which are implications. (Contributed by Alan Sare, 28-Aug-2016.)

Hypotheses

Ref	Expression
mp3an2i.1	|- ph
mp3an2i.2	|- ( ps -> ch )
mp3an2i.3	|- ( ps -> th )
mp3an2i.4	|- ( ( ph /\ ch /\ th ) -> ta )

Assertion

Ref	Expression
mp3an2i	|- ( ps -> ta )

Proof of Theorem mp3an2i

Step	Hyp	Ref	Expression
1		mp3an2i.2	. 2 |- ( ps -> ch )
2		mp3an2i.3	. 2 |- ( ps -> th )
3		mp3an2i.1	. . 3 |- ph
4		mp3an2i.4	. . 3 |- ( ( ph /\ ch /\ th ) -> ta )
5	3, 4	mp3an1 1255	. 2 |- ( ( ch /\ th ) -> ta )
6	1, 2, 5	syl2anc 403	1 |- ( ps -> ta )

Syntax hints:   -> wi 4   /\ w3a 919

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115  df-3an 921

This theorem is referenced by:  nnledivrp  8837  gcdn0gt0  10369  divgcdodd  10522  sqpweven  10553  2sqpwodd  10554