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Theorem or4 923
Description: Rearrangement of 4 disjuncts. (Contributed by NM, 12-Aug-1994.)
Assertion
Ref Expression
or4 (((𝜑𝜓) ∨ (𝜒𝜃)) ↔ ((𝜑𝜒) ∨ (𝜓𝜃)))

Proof of Theorem or4
StepHypRef Expression
1 or12 917 . . 3 ((𝜓 ∨ (𝜒𝜃)) ↔ (𝜒 ∨ (𝜓𝜃)))
21orbi2i 909 . 2 ((𝜑 ∨ (𝜓 ∨ (𝜒𝜃))) ↔ (𝜑 ∨ (𝜒 ∨ (𝜓𝜃))))
3 orass 918 . 2 (((𝜑𝜓) ∨ (𝜒𝜃)) ↔ (𝜑 ∨ (𝜓 ∨ (𝜒𝜃))))
4 orass 918 . 2 (((𝜑𝜒) ∨ (𝜓𝜃)) ↔ (𝜑 ∨ (𝜒 ∨ (𝜓𝜃))))
52, 3, 43bitr4i 305 1 (((𝜑𝜓) ∨ (𝜒𝜃)) ↔ ((𝜑𝜒) ∨ (𝜓𝜃)))
Colors of variables: wff setvar class
Syntax hints:  wb 208  wo 843
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 209  df-or 844
This theorem is referenced by:  or42  924  orordi  925  orordir  926  3or6  1443  swoer  8297  xmullem2  12637  swrdnnn0nd  13998  clsk1indlem3  40528
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