Theorem sylan9

Description: Nested syllogism inference conjoining dissimilar antecedents. (Contributed by NM, 14-May-1993) (Proof shortened by Andrew Salmon, 7-May-2011)

	Ref	Expression
Hypotheses	sylan9.1	|- ( ph -> ( ps -> ch ) )
	sylan9.2	|- ( th -> ( ch -> ta ) )
Assertion	sylan9	|- ( ( ph /\ th ) -> ( ps -> ta ) )

Proof

Step	Hyp	Ref	Expression
1		sylan9.1	|- ( ph -> ( ps -> ch ) )
2		sylan9.2	|- ( th -> ( ch -> ta ) )
3	1 2	syl9	|- ( ph -> ( th -> ( ps -> ta ) ) )
4	3	imp	|- ( ( ph /\ th ) -> ( ps -> ta ) )