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Theorem or42 724
Description: Rearrangement of 4 disjuncts. (Contributed by NM, 10-Jan-2005.)
Assertion
Ref Expression
or42 (((𝜑𝜓) ∨ (𝜒𝜃)) ↔ ((𝜑𝜒) ∨ (𝜃𝜓)))

Proof of Theorem or42
StepHypRef Expression
1 or4 723 . 2 (((𝜑𝜓) ∨ (𝜒𝜃)) ↔ ((𝜑𝜒) ∨ (𝜓𝜃)))
2 orcom 682 . . 3 ((𝜓𝜃) ↔ (𝜃𝜓))
32orbi2i 714 . 2 (((𝜑𝜒) ∨ (𝜓𝜃)) ↔ ((𝜑𝜒) ∨ (𝜃𝜓)))
41, 3bitri 182 1 (((𝜑𝜓) ∨ (𝜒𝜃)) ↔ ((𝜑𝜒) ∨ (𝜃𝜓)))
Colors of variables: wff set class
Syntax hints:  wb 103  wo 664
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  reapcotr  8051
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