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Theorem 3ancomb 893
Description: Commutation law for triple conjunction. (Contributed by NM, 21-Apr-1994.)
Assertion
Ref Expression
3ancomb ((𝜑𝜓𝜒) ↔ (𝜑𝜒𝜓))

Proof of Theorem 3ancomb
StepHypRef Expression
1 3ancoma 892 . 2 ((𝜑𝜓𝜒) ↔ (𝜓𝜑𝜒))
2 3anrot 890 . 2 ((𝜓𝜑𝜒) ↔ (𝜑𝜒𝜓))
31, 2bitri 173 1 ((𝜑𝜓𝜒) ↔ (𝜑𝜒𝜓))
Colors of variables: wff set class
Syntax hints:  wb 98  w3a 885
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110  df-3an 887
This theorem is referenced by:  3simpb  902  addcanprg  6712  elioore  8779
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