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Theorem an43 862
Description: Rearrangement of 4 conjuncts. (Contributed by Rodolfo Medina, 24-Sep-2010.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Assertion
Ref Expression
an43 (((𝜑𝜓) ∧ (𝜒𝜃)) ↔ ((𝜑𝜃) ∧ (𝜓𝜒)))

Proof of Theorem an43
StepHypRef Expression
1 an42 861 . 2 (((𝜑𝜃) ∧ (𝜓𝜒)) ↔ ((𝜑𝜓) ∧ (𝜒𝜃)))
21bicomi 212 1 (((𝜑𝜓) ∧ (𝜒𝜃)) ↔ ((𝜑𝜃) ∧ (𝜓𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wb 194  wa 382
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 195  df-an 384
This theorem is referenced by:  an3  863  prtlem15  32978
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