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Theorem 3anrot 901
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 257 . 2 ((𝜑 ∧ (𝜓𝜒)) ↔ ((𝜓𝜒) ∧ 𝜑))
2 3anass 900 . 2 ((𝜑𝜓𝜒) ↔ (𝜑 ∧ (𝜓𝜒)))
3 df-3an 898 . 2 ((𝜓𝜒𝜑) ↔ ((𝜓𝜒) ∧ 𝜑))
41, 2, 33bitr4i 205 1 ((𝜑𝜓𝜒) ↔ (𝜓𝜒𝜑))
Colors of variables: wff set class
Syntax hints:  wa 101  wb 102  w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  3ancomb  904  3anrev  906  3simpc  914  caovlem2d  5720  nnmcan  6122  modmulconst  10138
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