Theorem sylancl

Description: Syllogism inference combined with modus ponens. (Contributed by Jeff Madsen, 2-Sep-2009)

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

Proof

Step	Hyp	Ref	Expression
1		sylancl.1	|- ( ph -> ps )
2		sylancl.2	|- ch
3		sylancl.3	|- ( ( ps /\ ch ) -> th )
4	2	a1i	|- ( ph -> ch )
5	1 4 3	syl2anc	|- ( ph -> th )