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Theorem an4com24 43767
Description: Rearrangement of 4 conjuncts: second and forth positions interchanged. (Contributed by AV, 18-Feb-2022.)
Assertion
Ref Expression
an4com24 (((𝜑𝜓) ∧ (𝜒𝜃)) ↔ ((𝜑𝜃) ∧ (𝜒𝜓)))

Proof of Theorem an4com24
StepHypRef Expression
1 an43 657 . 2 (((𝜑𝜓) ∧ (𝜒𝜃)) ↔ ((𝜑𝜃) ∧ (𝜓𝜒)))
2 ancom 464 . . 3 ((𝜓𝜒) ↔ (𝜒𝜓))
32anbi2i 625 . 2 (((𝜑𝜃) ∧ (𝜓𝜒)) ↔ ((𝜑𝜃) ∧ (𝜒𝜓)))
41, 3bitri 278 1 (((𝜑𝜓) ∧ (𝜒𝜃)) ↔ ((𝜑𝜃) ∧ (𝜒𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wb 209  wa 399
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
This theorem is referenced by:  3an4ancom24  43768
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