Theorem syl2and

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

	Ref	Expression
Hypotheses	syl2and.1	|- ( ph -> ( ps -> ch ) )
	syl2and.2	|- ( ph -> ( th -> ta ) )
	syl2and.3	|- ( ph -> ( ( ch /\ ta ) -> et ) )
Assertion	syl2and	|- ( ph -> ( ( ps /\ th ) -> et ) )

Proof

Step	Hyp	Ref	Expression
1		syl2and.1	|- ( ph -> ( ps -> ch ) )
2		syl2and.2	|- ( ph -> ( th -> ta ) )
3		syl2and.3	|- ( ph -> ( ( ch /\ ta ) -> et ) )
4	2 3	sylan2d	|- ( ph -> ( ( ch /\ th ) -> et ) )
5	1 4	syland	|- ( ph -> ( ( ps /\ th ) -> et ) )