Theorem mp3an3an

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

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

Proof

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