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Theorem or32 513
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 510 . 2 (((φ ψ) χ) ↔ (φ (ψ χ)))
2 or12 509 . 2 ((φ (ψ χ)) ↔ (ψ (φ χ)))
3 orcom 376 . 2 ((ψ (φ χ)) ↔ ((φ χ) ψ))
41, 2, 33bitri 262 1 (((φ ψ) χ) ↔ ((φ χ) ψ))
Colors of variables: wff setvar class
Syntax hints:  wb 176   wo 357
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 177  df-or 359
This theorem is referenced by:  sspsstri  3371  sfin111  4536
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