Theorem 3anbi1i 1095

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 160	. 2 |- ( ch <-> ch )
3		biid 160	. 2 |- ( th <-> th )
4	1, 2, 3	3anbi123i 1093	1 |- ( ( ph /\ ch /\ th ) <-> ( ps /\ ch /\ th ) )

Syntax hints:   <-> wb 98   /\ w3a 885

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-3an 887

This theorem is referenced by:  fzolb  9009