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Theorem 3an4ancom24 43751
Description: Commutative law for a conjunction with a triple conjunction: second and forth positions interchanged. (Contributed by AV, 18-Feb-2022.)
Assertion
Ref Expression
3an4ancom24 (((𝜑𝜓𝜒) ∧ 𝜃) ↔ ((𝜑𝜃𝜒) ∧ 𝜓))

Proof of Theorem 3an4ancom24
StepHypRef Expression
1 an4com24 43750 . 2 (((𝜑𝜓) ∧ (𝜒𝜃)) ↔ ((𝜑𝜃) ∧ (𝜒𝜓)))
2 3an4anass 1102 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) ↔ ((𝜑𝜓) ∧ (𝜒𝜃)))
3 3an4anass 1102 . 2 (((𝜑𝜃𝜒) ∧ 𝜓) ↔ ((𝜑𝜃) ∧ (𝜒𝜓)))
41, 2, 33bitr4i 306 1 (((𝜑𝜓𝜒) ∧ 𝜃) ↔ ((𝜑𝜃𝜒) ∧ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  wb 209  wa 399  w3a 1084
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 210  df-an 400  df-3an 1086
This theorem is referenced by: (None)
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