Theorem mpsyl

Description: Modus ponens combined with a syllogism inference. (Contributed by Alan Sare, 20-Apr-2011)

	Ref	Expression
Hypotheses	mpsyl.1	|- ph
	mpsyl.2	|- ( ps -> ch )
	mpsyl.3	|- ( ph -> ( ch -> th ) )
Assertion	mpsyl	|- ( ps -> th )

Proof

Step	Hyp	Ref	Expression
1		mpsyl.1	|- ph
2		mpsyl.2	|- ( ps -> ch )
3		mpsyl.3	|- ( ph -> ( ch -> th ) )
4	1	a1i	|- ( ps -> ph )
5	4 2 3	sylc	|- ( ps -> th )