Theorem sylani

Description: A syllogism inference. (Contributed by NM, 2-May-1996)

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

Proof

Step	Hyp	Ref	Expression
1		sylani.1	|- ( ph -> ch )
2		sylani.2	|- ( ps -> ( ( ch /\ th ) -> ta ) )
3	1	a1i	|- ( ps -> ( ph -> ch ) )
4	3 2	syland	|- ( ps -> ( ( ph /\ th ) -> ta ) )