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Theorem orass 683
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 646 . 2 (((φ ψ) χ) ↔ (χ (φ ψ)))
2 or12 682 . 2 ((χ (φ ψ)) ↔ (φ (χ ψ)))
3 orcom 646 . . 3 ((χ ψ) ↔ (ψ χ))
43orbi2i 678 . 2 ((φ (χ ψ)) ↔ (φ (ψ χ)))
51, 2, 43bitri 195 1 (((φ ψ) χ) ↔ (φ (ψ χ)))
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:  pm2.31  684  pm2.32  685  or32  686  or4  687  3orass  887  dveeq2  1693  dveeq2or  1694  sbequilem  1716  dvelimALT  1883  dvelimfv  1884  dvelimor  1891  unass  3094  ltxr  8425
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