Theorem 3anbi1i 1142

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

Hypothesis

Ref	Expression
3anbi1i.1	|- (ph <-> ps)

Assertion

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

Proof of Theorem 3anbi1i

Step	Hyp	Ref	Expression
1		3anbi1i.1	. 2 |- (ph <-> ps)
2		biid 227	. 2 |- (ch <-> ch)
3		biid 227	. 2 |- (th <-> th)
4	1, 2, 3	3anbi123i 1140	1 |- ((ph /\ ch /\ th) <-> (ps /\ ch /\ th))

Syntax hints:   <-> wb 176   /\ w3a 934

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936

This theorem is referenced by:  brsnsi1  5776