Theorem mp3an1i

Description: An inference based on modus ponens. (Contributed by NM, 5-Jul-2005)

	Ref	Expression
Hypotheses	mp3an1i.1	|- ps
	mp3an1i.2	|- ( ph -> ( ( ps /\ ch /\ th ) -> ta ) )
Assertion	mp3an1i	|- ( ph -> ( ( ch /\ th ) -> ta ) )

Proof

Step	Hyp	Ref	Expression
1		mp3an1i.1	|- ps
2		mp3an1i.2	|- ( ph -> ( ( ps /\ ch /\ th ) -> ta ) )
3	2	com12	|- ( ( ps /\ ch /\ th ) -> ( ph -> ta ) )
4	1 3	mp3an1	|- ( ( ch /\ th ) -> ( ph -> ta ) )
5	4	com12	|- ( ph -> ( ( ch /\ th ) -> ta ) )