Theorem sylan2d

Description: A syllogism deduction. (Contributed by NM, 15-Dec-2004)

	Ref	Expression
Hypotheses	sylan2d.1	|- ( ph -> ( ps -> ch ) )
	sylan2d.2	|- ( ph -> ( ( th /\ ch ) -> ta ) )
Assertion	sylan2d	|- ( ph -> ( ( th /\ ps ) -> ta ) )

Proof

Step	Hyp	Ref	Expression
1		sylan2d.1	|- ( ph -> ( ps -> ch ) )
2		sylan2d.2	|- ( ph -> ( ( th /\ ch ) -> ta ) )
3	2	ancomsd	|- ( ph -> ( ( ch /\ th ) -> ta ) )
4	1 3	syland	|- ( ph -> ( ( ps /\ th ) -> ta ) )
5	4	ancomsd	|- ( ph -> ( ( th /\ ps ) -> ta ) )