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Theorem 3ancoma 954
Description: Commutation law for triple conjunction. (Contributed by NM, 21-Apr-1994.)
Assertion
Ref Expression
3ancoma ((𝜑𝜓𝜒) ↔ (𝜓𝜑𝜒))

Proof of Theorem 3ancoma
StepHypRef Expression
1 ancom 264 . . 3 ((𝜑𝜓) ↔ (𝜓𝜑))
21anbi1i 453 . 2 (((𝜑𝜓) ∧ 𝜒) ↔ ((𝜓𝜑) ∧ 𝜒))
3 df-3an 949 . 2 ((𝜑𝜓𝜒) ↔ ((𝜑𝜓) ∧ 𝜒))
4 df-3an 949 . 2 ((𝜓𝜑𝜒) ↔ ((𝜓𝜑) ∧ 𝜒))
52, 3, 43bitr4i 211 1 ((𝜑𝜓𝜒) ↔ (𝜓𝜑𝜒))
Colors of variables: wff set class
Syntax hints:  wa 103  wb 104  w3a 947
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 949
This theorem is referenced by:  3ancomb  955  3anrev  957  3anan12  959  3com12  1170  elfzmlbp  9877  elfzo2  9895
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