Theorem 3anbi3d

Description: Deduction adding conjuncts to an equivalence. (Contributed by NM, 8-Sep-2006)

	Ref	Expression
Hypothesis	3anbi1d.1	|- ( ph -> ( ps <-> ch ) )
Assertion	3anbi3d	|- ( ph -> ( ( th /\ ta /\ ps ) <-> ( th /\ ta /\ ch ) ) )

Proof

Step	Hyp	Ref	Expression
1		3anbi1d.1	|- ( ph -> ( ps <-> ch ) )
2		biidd	|- ( ph -> ( th <-> th ) )
3	2 1	3anbi13d	|- ( ph -> ( ( th /\ ta /\ ps ) <-> ( th /\ ta /\ ch ) ) )