Theorem sylancom

Description: Syllogism inference with commutation of antecedents. (Contributed by NM, 2-Jul-2008)

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

Proof

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