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Theorem 3anan12 985
Description: Convert triple conjunction to conjunction, then commute. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)
Assertion
Ref Expression
3anan12 ((𝜑𝜓𝜒) ↔ (𝜓 ∧ (𝜑𝜒)))

Proof of Theorem 3anan12
StepHypRef Expression
1 3ancoma 980 . 2 ((𝜑𝜓𝜒) ↔ (𝜓𝜑𝜒))
2 3anass 977 . 2 ((𝜓𝜑𝜒) ↔ (𝜓 ∧ (𝜑𝜒)))
31, 2bitri 183 1 ((𝜑𝜓𝜒) ↔ (𝜓 ∧ (𝜑𝜒)))
Colors of variables: wff set class
Syntax hints:  wa 103  wb 104  w3a 973
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 975
This theorem is referenced by:  fncnv  5262  dff1o2  5445
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