Theorem sylan9bbr

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

	Ref	Expression
Hypotheses	sylan9bbr.1	|- ( ph -> ( ps <-> ch ) )
	sylan9bbr.2	|- ( th -> ( ch <-> ta ) )
Assertion	sylan9bbr	|- ( ( th /\ ph ) -> ( ps <-> ta ) )

Proof

Step	Hyp	Ref	Expression
1		sylan9bbr.1	|- ( ph -> ( ps <-> ch ) )
2		sylan9bbr.2	|- ( th -> ( ch <-> ta ) )
3	1 2	sylan9bb	|- ( ( ph /\ th ) -> ( ps <-> ta ) )
4	3	ancoms	|- ( ( th /\ ph ) -> ( ps <-> ta ) )