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Theorem 3an6 1401
 Description: Analogue of an4 861 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 1400 . 2 (((𝜑𝜒𝜏) ∧ (𝜓𝜃𝜂)) ↔ ((𝜑𝜓) ∧ (𝜒𝜃) ∧ (𝜏𝜂)))
21bicomi 213 1 (((𝜑𝜓) ∧ (𝜒𝜃) ∧ (𝜏𝜂)) ↔ ((𝜑𝜒𝜏) ∧ (𝜓𝜃𝜂)))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 195   ∧ wa 383   ∧ w3a 1031 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 196  df-an 385  df-3an 1033 This theorem is referenced by:  an33rean  1438  f13dfv  6430  poxp  7176  wfrlem4  7305  cotr2g  13563  axcontlem8  25651  cusgra3v  25993  cgr3tr4  31329  cplgr3v  40657
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