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Theorem 3anbi1i 1172
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
3anbi1i ((𝜑𝜒𝜃) ↔ (𝜓𝜒𝜃))

Proof of Theorem 3anbi1i
StepHypRef Expression
1 3anbi1i.1 . 2 (𝜑𝜓)
2 biid 170 . 2 (𝜒𝜒)
3 biid 170 . 2 (𝜃𝜃)
41, 2, 33anbi123i 1170 1 ((𝜑𝜒𝜃) ↔ (𝜓𝜒𝜃))
Colors of variables: wff set class
Syntax hints:  wb 104  w3a 962
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 964
This theorem is referenced by:  fzolb  9923  txcn  12433
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