Theorem 3anbi12d

Description: Deduction conjoining and adding a conjunct to equivalences. (Contributed by NM, 8-Sep-2006)

	Ref	Expression
Hypotheses	3anbi12d.1	|- ( ph -> ( ps <-> ch ) )
	3anbi12d.2	|- ( ph -> ( th <-> ta ) )
Assertion	3anbi12d	|- ( ph -> ( ( ps /\ th /\ et ) <-> ( ch /\ ta /\ et ) ) )

Proof

Step	Hyp	Ref	Expression
1		3anbi12d.1	|- ( ph -> ( ps <-> ch ) )
2		3anbi12d.2	|- ( ph -> ( th <-> ta ) )
3		biidd	|- ( ph -> ( et <-> et ) )
4	1 2 3	3anbi123d	|- ( ph -> ( ( ps /\ th /\ et ) <-> ( ch /\ ta /\ et ) ) )