ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm2.25dc Structured version   GIF version

Theorem pm2.25dc 791
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 742 . 2 (DECID φ ↔ (φ ¬ φ))
2 orel1 643 . . 3 φ → ((φ ψ) → ψ))
32orim2i 677 . 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 628  DECID wdc 741
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 545  ax-io 629
This theorem depends on definitions:  df-bi 110  df-dc 742
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator