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Theorem orel1 631
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 pm2.53 628 . 2 ((φ ψ) → (¬ φψ))
21com12 27 1 φ → ((φ ψ) → ψ))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   wo 616
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-in2 533  ax-io 617
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  biorf  650  pm2.25dc  785  pm2.85dc  804  euor2  1939  prel12  3494  funun  4837  acexmidlema  5396  acexmidlemb  5397
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