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Theorem anandi3r 1104
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 1098 . 2 ((𝜑𝜓𝜒) ↔ ((𝜑𝜒) ∧ 𝜓))
2 anandir 676 . 2 (((𝜑𝜒) ∧ 𝜓) ↔ ((𝜑𝜓) ∧ (𝜒𝜓)))
31, 2bitri 275 1 ((𝜑𝜓𝜒) ↔ ((𝜑𝜓) ∧ (𝜒𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wb 205  wa 397  w3a 1088
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 398  df-3an 1090
This theorem is referenced by:  refsymrel2  37079  refsymrel3  37080  dfeqvrel2  37102  dfeqvrel3  37103  i0oii  47042  alsi-no-surprise  47333
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