Theorem syl2ani

Description: A syllogism inference. (Contributed by NM, 3-Aug-1999)

	Ref	Expression
Hypotheses	syl2ani.1	|- ( ph -> ch )
	syl2ani.2	|- ( et -> th )
	syl2ani.3	|- ( ps -> ( ( ch /\ th ) -> ta ) )
Assertion	syl2ani	|- ( ps -> ( ( ph /\ et ) -> ta ) )

Proof

Step	Hyp	Ref	Expression
1		syl2ani.1	|- ( ph -> ch )
2		syl2ani.2	|- ( et -> th )
3		syl2ani.3	|- ( ps -> ( ( ch /\ th ) -> ta ) )
4	2 3	sylan2i	|- ( ps -> ( ( ch /\ et ) -> ta ) )
5	1 4	sylani	|- ( ps -> ( ( ph /\ et ) -> ta ) )