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Theorem anandi3r 1100
Description: Distribution of triple conjunction over conjunction. (Contributed by David A. Wheeler, 4-Nov-2018.)
Assertion
Ref Expression
anandi3r ((𝜑𝜓𝜒) ↔ ((𝜑𝜓) ∧ (𝜒𝜓)))

Proof of Theorem anandi3r
StepHypRef Expression
1 3anan32 1094 . 2 ((𝜑𝜓𝜒) ↔ ((𝜑𝜒) ∧ 𝜓))
2 anandir 676 . 2 (((𝜑𝜒) ∧ 𝜓) ↔ ((𝜑𝜓) ∧ (𝜒𝜓)))
31, 2bitri 278 1 ((𝜑𝜓𝜒) ↔ ((𝜑𝜓) ∧ (𝜒𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wb 209  wa 399  w3a 1084
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 210  df-an 400  df-3an 1086
This theorem is referenced by:  refsymrel2  35873  refsymrel3  35874  dfeqvrel2  35895  dfeqvrel3  35896  alsi-no-surprise  45175
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