Theorem syl2anc

Description: Syllogism inference combined with contraction. (Contributed by NM, 16-Mar-2012)

	Ref	Expression
Hypotheses	syl2anc.1	|- ( ph -> ps )
	syl2anc.2	|- ( ph -> ch )
	syl2anc.3	|- ( ( ps /\ ch ) -> th )
Assertion	syl2anc	|- ( ph -> th )

Proof

Step	Hyp	Ref	Expression
1		syl2anc.1	|- ( ph -> ps )
2		syl2anc.2	|- ( ph -> ch )
3		syl2anc.3	|- ( ( ps /\ ch ) -> th )
4	3	ex	|- ( ps -> ( ch -> th ) )
5	1 2 4	sylc	|- ( ph -> th )