Theorem sylan9r

Description: Nested syllogism inference conjoining dissimilar antecedents. (Contributed by NM, 14-May-1993)

	Ref	Expression
Hypotheses	sylan9r.1	|- ( ph -> ( ps -> ch ) )
	sylan9r.2	|- ( th -> ( ch -> ta ) )
Assertion	sylan9r	|- ( ( th /\ ph ) -> ( ps -> ta ) )

Proof

Step	Hyp	Ref	Expression
1		sylan9r.1	|- ( ph -> ( ps -> ch ) )
2		sylan9r.2	|- ( th -> ( ch -> ta ) )
3	1 2	syl9r	|- ( th -> ( ph -> ( ps -> ta ) ) )
4	3	imp	|- ( ( th /\ ph ) -> ( ps -> ta ) )