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Theorem anandi3r 1102
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 1096 . 2 ((𝜑𝜓𝜒) ↔ ((𝜑𝜒) ∧ 𝜓))
2 anandir 674 . 2 (((𝜑𝜒) ∧ 𝜓) ↔ ((𝜑𝜓) ∧ (𝜒𝜓)))
31, 2bitri 274 1 ((𝜑𝜓𝜒) ↔ ((𝜑𝜓) ∧ (𝜒𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wb 205  wa 396  w3a 1086
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 206  df-an 397  df-3an 1088
This theorem is referenced by:  refsymrel2  36678  refsymrel3  36679  dfeqvrel2  36700  dfeqvrel3  36701  i0oii  46180  alsi-no-surprise  46467
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