ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3anbi2i GIF version

Theorem 3anbi2i 1135
Description: Inference adding two conjuncts to each side of a biconditional. (Contributed by NM, 8-Sep-2006.)
Hypothesis
Ref Expression
3anbi1i.1 (𝜑𝜓)
Assertion
Ref Expression
3anbi2i ((𝜒𝜑𝜃) ↔ (𝜒𝜓𝜃))

Proof of Theorem 3anbi2i
StepHypRef Expression
1 biid 169 . 2 (𝜒𝜒)
2 3anbi1i.1 . 2 (𝜑𝜓)
3 biid 169 . 2 (𝜃𝜃)
41, 2, 33anbi123i 1132 1 ((𝜒𝜑𝜃) ↔ (𝜒𝜓𝜃))
Colors of variables: wff set class
Syntax hints:  wb 103  w3a 924
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 926
This theorem is referenced by:  seq3f1olemp  9927  seq3f1oleml  9928  fisum  10774
  Copyright terms: Public domain W3C validator