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Theorem orass 510
Description: Associative law for disjunction. Theorem *4.33 of [WhiteheadRussell] p. 118. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
orass (((φ ψ) χ) ↔ (φ (ψ χ)))

Proof of Theorem orass
StepHypRef Expression
1 orcom 376 . 2 (((φ ψ) χ) ↔ (χ (φ ψ)))
2 or12 509 . 2 ((χ (φ ψ)) ↔ (φ (χ ψ)))
3 orcom 376 . . 3 ((χ ψ) ↔ (ψ χ))
43orbi2i 505 . 2 ((φ (χ ψ)) ↔ (φ (ψ χ)))
51, 2, 43bitri 262 1 (((φ ψ) χ) ↔ (φ (ψ χ)))
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:  pm2.31  511  pm2.32  512  or32  513  or4  514  3orass  937  axi12  2333  unass  3420
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