Theorem mp3an12i

Description: mp3an with antecedents in standard conjunction form and with one hypothesis an implication. (Contributed by Alan Sare, 28-Aug-2016)

	Ref	Expression
Hypotheses	mp3an12i.1	|- ph
	mp3an12i.2	|- ps
	mp3an12i.3	|- ( ch -> th )
	mp3an12i.4	|- ( ( ph /\ ps /\ th ) -> ta )
Assertion	mp3an12i	|- ( ch -> ta )

Proof

Step	Hyp	Ref	Expression
1		mp3an12i.1	|- ph
2		mp3an12i.2	|- ps
3		mp3an12i.3	|- ( ch -> th )
4		mp3an12i.4	|- ( ( ph /\ ps /\ th ) -> ta )
5	1 2 4	mp3an12	|- ( th -> ta )
6	3 5	syl	|- ( ch -> ta )