Theorem 3anbi3i 1144

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
3anbi3i	|- ((ch /\ th /\ ph) <-> (ch /\ th /\ ps))

Proof of Theorem 3anbi3i

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

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:  sfin112  4530  dfsi2  4752  cnvsi  5519