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Theorem 3anrot 983
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 266 . 2 ((𝜑 ∧ (𝜓𝜒)) ↔ ((𝜓𝜒) ∧ 𝜑))
2 3anass 982 . 2 ((𝜑𝜓𝜒) ↔ (𝜑 ∧ (𝜓𝜒)))
3 df-3an 980 . 2 ((𝜓𝜒𝜑) ↔ ((𝜓𝜒) ∧ 𝜑))
41, 2, 33bitr4i 212 1 ((𝜑𝜓𝜒) ↔ (𝜓𝜒𝜑))
Colors of variables: wff set class
Syntax hints:  wa 104  wb 105  w3a 978
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-3an 980
This theorem is referenced by:  3ancomb  986  3anrev  988  3simpc  996  caovlem2d  6061  nnmcan  6514  modmulconst  11811  srgrmhm  13000  xmetpsmet  13529  comet  13659  lgsdi  14098
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