Theorem bi2anan9

Description: Deduction joining two equivalences to form equivalence of conjunctions. (Contributed by NM, 31-Jul-1995)

	Ref	Expression
Hypotheses	bi2an9.1	|- ( ph -> ( ps <-> ch ) )
	bi2an9.2	|- ( th -> ( ta <-> et ) )
Assertion	bi2anan9	|- ( ( ph /\ th ) -> ( ( ps /\ ta ) <-> ( ch /\ et ) ) )

Proof

Step	Hyp	Ref	Expression
1		bi2an9.1	|- ( ph -> ( ps <-> ch ) )
2		bi2an9.2	|- ( th -> ( ta <-> et ) )
3		pm4.38	|- ( ( ( ps <-> ch ) /\ ( ta <-> et ) ) -> ( ( ps /\ ta ) <-> ( ch /\ et ) ) )
4	1 2 3	syl2an	|- ( ( ph /\ th ) -> ( ( ps /\ ta ) <-> ( ch /\ et ) ) )