Theorem syland

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

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

Proof

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