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Theorem pm2.25dc 785
Description: Elimination of disjunction based on a disjunction, for a decidable proposition. Based on theorem *2.25 of [WhiteheadRussell] p. 104. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm2.25dc (DECID φ → (φ ((φ ψ) → ψ)))

Proof of Theorem pm2.25dc
StepHypRef Expression
1 df-dc 734 . 2 (DECID φ ↔ (φ ¬ φ))
2 orel1 631 . . 3 φ → ((φ ψ) → ψ))
32orim2i 665 . 2 ((φ ¬ φ) → (φ ((φ ψ) → ψ)))
41, 3sylbi 114 1 (DECID φ → (φ ((φ ψ) → ψ)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   wo 616  DECID wdc 733
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  df-dc 734
This theorem is referenced by: (None)
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