Theorem sylan9bb

Description: Nested syllogism inference conjoining dissimilar antecedents. (Contributed by NM, 4-Mar-1995)

	Ref	Expression
Hypotheses	sylan9bb.1	|- ( ph -> ( ps <-> ch ) )
	sylan9bb.2	|- ( th -> ( ch <-> ta ) )
Assertion	sylan9bb	|- ( ( ph /\ th ) -> ( ps <-> ta ) )

Proof

Step	Hyp	Ref	Expression
1		sylan9bb.1	|- ( ph -> ( ps <-> ch ) )
2		sylan9bb.2	|- ( th -> ( ch <-> ta ) )
3	1	adantr	|- ( ( ph /\ th ) -> ( ps <-> ch ) )
4	2	adantl	|- ( ( ph /\ th ) -> ( ch <-> ta ) )
5	3 4	bitrd	|- ( ( ph /\ th ) -> ( ps <-> ta ) )