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Theorem orel2 372
Description: Elimination of disjunction by denial of a disjunct. Theorem *2.56 of [WhiteheadRussell] p. 107. (Contributed by NM, 12-Aug-1994.) (Proof shortened by Wolf Lammen, 5-Apr-2013.)
Assertion
Ref Expression
orel2 φ → ((ψ φ) → ψ))

Proof of Theorem orel2
StepHypRef Expression
1 idd 21 . 2 φ → (ψψ))
2 pm2.21 100 . 2 φ → (φψ))
31, 2jaod 369 1 φ → ((ψ φ) → 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:  biorfi  396  pm2.64  764  pm2.74  819  pm5.71  902  nndisjeq  4429  xpcan2  5058  funun  5146  enadjlem1  6059  enadj  6060
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