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Theorem or42 550
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 549 . 2 (((𝜑𝜓) ∨ (𝜒𝜃)) ↔ ((𝜑𝜒) ∨ (𝜓𝜃)))
2 orcom 401 . . 3 ((𝜓𝜃) ↔ (𝜃𝜓))
32orbi2i 540 . 2 (((𝜑𝜒) ∨ (𝜓𝜃)) ↔ ((𝜑𝜒) ∨ (𝜃𝜓)))
41, 3bitri 264 1 (((𝜑𝜓) ∨ (𝜒𝜃)) ↔ ((𝜑𝜒) ∨ (𝜃𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wo 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 197  df-or 384
This theorem is referenced by:  clsk1indlem3  38658
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