Theorem 3anbi2i 1254

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
3anbi2i	|- ( ( ch /\ ph /\ th ) <-> ( ch /\ ps /\ th ) )

Proof of Theorem 3anbi2i

Step	Hyp	Ref	Expression
1		biid 251	. 2 |- ( ch <-> ch )
2		3anbi1i.1	. 2 |- ( ph <-> ps )
3		biid 251	. 2 |- ( th <-> th )
4	1, 2, 3	3anbi123i 1251	1 |- ( ( ch /\ ph /\ th ) <-> ( ch /\ ps /\ th ) )

Syntax hints:   <-> wb 196   /\ w3a 1037

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 197  df-an 386  df-3an 1039

This theorem is referenced by:  f13dfv  6530  axgroth4  9654  fi1uzind  13279  fi1uzindOLD  13285  bnj543  30963  bnj916  31003  topdifinffinlem  33195