Theorem anbi12d

Description: Deduction joining two equivalences to form equivalence of conjunctions. (Contributed by NM, 26-May-1993)

	Ref	Expression
Hypotheses	anbi12d.1	|- ( ph -> ( ps <-> ch ) )
	anbi12d.2	|- ( ph -> ( th <-> ta ) )
Assertion	anbi12d	|- ( ph -> ( ( ps /\ th ) <-> ( ch /\ ta ) ) )

Proof

Step	Hyp	Ref	Expression
1		anbi12d.1	|- ( ph -> ( ps <-> ch ) )
2		anbi12d.2	|- ( ph -> ( th <-> ta ) )
3	1	anbi1d	|- ( ph -> ( ( ps /\ th ) <-> ( ch /\ th ) ) )
4	2	anbi2d	|- ( ph -> ( ( ch /\ th ) <-> ( ch /\ ta ) ) )
5	3 4	bitrd	|- ( ph -> ( ( ps /\ th ) <-> ( ch /\ ta ) ) )