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Theorem 3an6 1228
Description: Analog of an4 528 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 1227 . 2 (((𝜑𝜒𝜏) ∧ (𝜓𝜃𝜂)) ↔ ((𝜑𝜓) ∧ (𝜒𝜃) ∧ (𝜏𝜂)))
21bicomi 127 1 (((𝜑𝜓) ∧ (𝜒𝜃) ∧ (𝜏𝜂)) ↔ ((𝜑𝜒𝜏) ∧ (𝜓𝜃𝜂)))
Colors of variables: wff set class
Syntax hints:  wa 101  wb 102  w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  poxp  5880
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