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Theorem 3an6 1408
Description: Analogue of an4 865 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 1407 . 2 (((𝜑𝜒𝜏) ∧ (𝜓𝜃𝜂)) ↔ ((𝜑𝜓) ∧ (𝜒𝜃) ∧ (𝜏𝜂)))
21bicomi 214 1 (((𝜑𝜓) ∧ (𝜒𝜃) ∧ (𝜏𝜂)) ↔ ((𝜑𝜒𝜏) ∧ (𝜓𝜃𝜂)))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wa 384  w3a 1037
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 197  df-an 386  df-3an 1039
This theorem is referenced by:  an33rean  1445  f13dfv  6527  poxp  7286  wfrlem4  7415  cotr2g  13709  axcontlem8  25845  cplgr3v  26325  cgr3tr4  32143
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