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Theorem 3an6 1571
 Description: Analogue of an4 647 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 1570 . 2 (((𝜑𝜒𝜏) ∧ (𝜓𝜃𝜂)) ↔ ((𝜑𝜓) ∧ (𝜒𝜃) ∧ (𝜏𝜂)))
21bicomi 216 1 (((𝜑𝜓) ∧ (𝜒𝜃) ∧ (𝜏𝜂)) ↔ ((𝜑𝜒𝜏) ∧ (𝜓𝜃𝜂)))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 198   ∧ wa 385   ∧ w3a 1108 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 199  df-an 386  df-3an 1110 This theorem is referenced by:  an33rean  1608  f13dfv  6757  poxp  7525  wfrlem4  7655  wfrlem4OLD  7656  cotr2g  14055  axcontlem8  26201  cplgr3v  26678  cgr3tr4  32665
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