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Theorem 3an6 1322
Description: Analog of an4 586 for triple conjunction. (Contributed by Scott Fenton, 16-Mar-2011.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Assertion
Ref Expression
3an6 (((𝜑𝜓) ∧ (𝜒𝜃) ∧ (𝜏𝜂)) ↔ ((𝜑𝜒𝜏) ∧ (𝜓𝜃𝜂)))

Proof of Theorem 3an6
StepHypRef Expression
1 an6 1321 . 2 (((𝜑𝜒𝜏) ∧ (𝜓𝜃𝜂)) ↔ ((𝜑𝜓) ∧ (𝜒𝜃) ∧ (𝜏𝜂)))
21bicomi 132 1 (((𝜑𝜓) ∧ (𝜒𝜃) ∧ (𝜏𝜂)) ↔ ((𝜑𝜒𝜏) ∧ (𝜓𝜃𝜂)))
Colors of variables: wff set class
Syntax hints:  wa 104  wb 105  w3a 978
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-3an 980
This theorem is referenced by:  poxp  6232
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