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Theorem orel1 371
Description: Elimination of disjunction by denial of a disjunct. Theorem *2.55 of [WhiteheadRussell] p. 107. (Contributed by NM, 12-Aug-1994.) (Proof shortened by Wolf Lammen, 21-Jul-2012.)
Assertion
Ref Expression
orel1 φ → ((φ ψ) → ψ))

Proof of Theorem orel1
StepHypRef Expression
1 pm2.53 362 . 2 ((φ ψ) → (¬ φψ))
21com12 27 1 φ → ((φ ψ) → ψ))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4   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:  pm2.25  393  biorf  394  euor2  2272  nndisjeq  4429  nnceleq  4430  sfinltfin  4535  sfin111  4536  phialllem1  4616  xpcan  5057  funun  5146  enprmaplem3  6078
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