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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 (𝜑𝜓)
Assertion
Ref Expression
3anbi1i ((𝜑𝜒𝜃) ↔ (𝜓𝜒𝜃))

Proof of Theorem 3anbi1i
StepHypRef Expression
1 3anbi1i.1 . 2 (𝜑𝜓)
2 biid 160 . 2 (𝜒𝜒)
3 biid 160 . 2 (𝜃𝜃)
41, 2, 33anbi123i 1093 1 ((𝜑𝜒𝜃) ↔ (𝜓𝜒𝜃))
Colors of variables: wff set class
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
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