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Theorem 3anbi3i 1136
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
3anbi3i ((𝜒𝜃𝜑) ↔ (𝜒𝜃𝜓))

Proof of Theorem 3anbi3i
StepHypRef Expression
1 biid 169 . 2 (𝜒𝜒)
2 biid 169 . 2 (𝜃𝜃)
3 3anbi1i.1 . 2 (𝜑𝜓)
41, 2, 33anbi123i 1132 1 ((𝜒𝜃𝜑) ↔ (𝜒𝜃𝜓))
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:  dfer2  6273  cbvsum  10713
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