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Theorem 3anrot 968
Description: Rotation law for triple conjunction. (Contributed by NM, 8-Apr-1994.)
Assertion
Ref Expression
3anrot ((𝜑𝜓𝜒) ↔ (𝜓𝜒𝜑))

Proof of Theorem 3anrot
StepHypRef Expression
1 ancom 264 . 2 ((𝜑 ∧ (𝜓𝜒)) ↔ ((𝜓𝜒) ∧ 𝜑))
2 3anass 967 . 2 ((𝜑𝜓𝜒) ↔ (𝜑 ∧ (𝜓𝜒)))
3 df-3an 965 . 2 ((𝜓𝜒𝜑) ↔ ((𝜓𝜒) ∧ 𝜑))
41, 2, 33bitr4i 211 1 ((𝜑𝜓𝜒) ↔ (𝜓𝜒𝜑))
Colors of variables: wff set class
Syntax hints:  wa 103  wb 104  w3a 963
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 965
This theorem is referenced by:  3ancomb  971  3anrev  973  3simpc  981  caovlem2d  5970  nnmcan  6422  modmulconst  11559  xmetpsmet  12575  comet  12705
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