Theorem 3anbi1i

Description: Inference adding two conjuncts to each side of a biconditional. (Contributed by NM, 8-Sep-2006)

	Ref	Expression
Hypothesis	3anbi1i.1	|- ( ph <-> ps )
Assertion	3anbi1i	|- ( ( ph /\ ch /\ th ) <-> ( ps /\ ch /\ th ) )

Proof

Step	Hyp	Ref	Expression
1		3anbi1i.1	|- ( ph <-> ps )
2		biid	|- ( ch <-> ch )
3		biid	|- ( th <-> th )
4	1 2 3	3anbi123i	|- ( ( ph /\ ch /\ th ) <-> ( ps /\ ch /\ th ) )