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Theorem 3anbi1i 1142
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 ((φ χ θ) ↔ (ψ χ θ))

Proof of Theorem 3anbi1i
StepHypRef Expression
1 3anbi1i.1 . 2 (φψ)
2 biid 227 . 2 (χχ)
3 biid 227 . 2 (θθ)
41, 2, 33anbi123i 1140 1 ((φ χ θ) ↔ (ψ χ θ))
Colors of variables: wff setvar class
Syntax hints:  wb 176   w3a 934
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 177  df-an 360  df-3an 936
This theorem is referenced by:  brsnsi1  5775
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