ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm2.61dc GIF version

Theorem pm2.61dc 762
Description: Case elimination for a decidable proposition. Based on theorem *2.61 of [WhiteheadRussell] p. 107. (Contributed by Jim Kingdon, 29-Mar-2018.)
Assertion
Ref Expression
pm2.61dc (DECID 𝜑 → ((𝜑𝜓) → ((¬ 𝜑𝜓) → 𝜓)))

Proof of Theorem pm2.61dc
StepHypRef Expression
1 pm2.6dc 759 . 2 (DECID 𝜑 → ((¬ 𝜑𝜓) → ((𝜑𝜓) → 𝜓)))
21com23 72 1 (DECID 𝜑 → ((𝜑𝜓) → ((¬ 𝜑𝜓) → 𝜓)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  DECID wdc 742
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-io 630
This theorem depends on definitions:  df-bi 110  df-dc 743
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator