Theorem 3anbi1i 824

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

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

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

This theorem is referenced by:  istps5OLD 7610  lmfval 7925  ficli 10472  ficliOLD 10473

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