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Theorem 3ancoma 903
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 257 . . 3 ((𝜑𝜓) ↔ (𝜓𝜑))
21anbi1i 439 . 2 (((𝜑𝜓) ∧ 𝜒) ↔ ((𝜓𝜑) ∧ 𝜒))
3 df-3an 898 . 2 ((𝜑𝜓𝜒) ↔ ((𝜑𝜓) ∧ 𝜒))
4 df-3an 898 . 2 ((𝜓𝜑𝜒) ↔ ((𝜓𝜑) ∧ 𝜒))
52, 3, 43bitr4i 205 1 ((𝜑𝜓𝜒) ↔ (𝜓𝜑𝜒))
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  3anan12  908  3com12  1119  elfzmlbp  9091  elfzo2  9108
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