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Theorem anandi3 933
Description: Distribution of triple conjunction over conjunction. (Contributed by David A. Wheeler, 4-Nov-2018.)
Assertion
Ref Expression
anandi3 ((𝜑𝜓𝜒) ↔ ((𝜑𝜓) ∧ (𝜑𝜒)))

Proof of Theorem anandi3
StepHypRef Expression
1 3anass 924 . 2 ((𝜑𝜓𝜒) ↔ (𝜑 ∧ (𝜓𝜒)))
2 anandi 555 . 2 ((𝜑 ∧ (𝜓𝜒)) ↔ ((𝜑𝜓) ∧ (𝜑𝜒)))
31, 2bitri 182 1 ((𝜑𝜓𝜒) ↔ ((𝜑𝜓) ∧ (𝜑𝜒)))
Colors of variables: wff set class
Syntax hints:  wa 102  wb 103  w3a 920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 922
This theorem is referenced by: (None)
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