ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm4.62dc GIF version

Theorem pm4.62dc 868
Description: Implication in terms of disjunction. Like Theorem *4.62 of [WhiteheadRussell] p. 120, but for a decidable antecedent. (Contributed by Jim Kingdon, 21-Apr-2018.)
Assertion
Ref Expression
pm4.62dc (DECID 𝜑 → ((𝜑 → ¬ 𝜓) ↔ (¬ 𝜑 ∨ ¬ 𝜓)))

Proof of Theorem pm4.62dc
StepHypRef Expression
1 imordc 867 1 (DECID 𝜑 → ((𝜑 → ¬ 𝜓) ↔ (¬ 𝜑 ∨ ¬ 𝜓)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 104  wo 682  DECID wdc 804
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 588  ax-in2 589  ax-io 683
This theorem depends on definitions:  df-bi 116  df-dc 805
This theorem is referenced by:  ianordc  869
  Copyright terms: Public domain W3C validator