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Theorem or32 686
Description: A rearrangement of disjuncts. (Contributed by NM, 18-Oct-1995.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
or32 (((φ ψ) χ) ↔ ((φ χ) ψ))

Proof of Theorem or32
StepHypRef Expression
1 orass 683 . 2 (((φ ψ) χ) ↔ (φ (ψ χ)))
2 or12 682 . 2 ((φ (ψ χ)) ↔ (ψ (φ χ)))
3 orcom 646 . 2 ((ψ (φ χ)) ↔ ((φ χ) ψ))
41, 2, 33bitri 195 1 (((φ ψ) χ) ↔ ((φ χ) ψ))
Colors of variables: wff set class
Syntax hints:  wb 98   wo 628
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  xrnepnf  8470
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