Theorem 3anbi3i 826

Description: Inference adding two conjuncts to each side of a biconditional.

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		pm4.2 170	. 2 |- (ch <-> ch)
2		pm4.2 170	. 2 |- (th <-> th)
3		3anbi1i.1	. 2 |- (ph <-> ps)
4	1, 2, 3	3anbi123i 822	1 |- ((ch /\ th /\ ph) <-> (ch /\ th /\ ps))

Syntax hints:   <-> wb 146   /\ w3a 775

This theorem is referenced by:  efcn 7423  lmbr2 7929  axgroth2 8778

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225  df-3an 777

Copyright terms: Public domain