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

Theorem dfordc 790
Description: Definition of 'or' in terms of negation and implication for a decidable proposition. Based on definition of [Margaris] p. 49. One direction, pm2.53 640, holds for all propositions, not just decidable ones. (Contributed by Jim Kingdon, 26-Mar-2018.)
Assertion
Ref Expression
dfordc (DECID φ → ((φ ψ) ↔ (¬ φψ)))

Proof of Theorem dfordc
StepHypRef Expression
1 pm2.53 640 . 2 ((φ ψ) → (¬ φψ))
2 pm2.54dc 789 . 2 (DECID φ → ((¬ φψ) → (φ ψ)))
31, 2impbid2 131 1 (DECID φ → ((φ ψ) ↔ (¬ φψ)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 98   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-in1 544  ax-in2 545  ax-io 629
This theorem depends on definitions:  df-bi 110  df-dc 742
This theorem is referenced by:  imordc  795  pm4.64dc  800  pm5.17dc  809  pm5.6dc  834  pm3.12dc  864  pm5.15dc  1277  19.32dc  1566  r19.32vdc  2453  prime  8113
  Copyright terms: Public domain W3C validator