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Theorem dfordc 878
 Description: Definition of disjunction in terms of negation and implication for a decidable proposition. Based on definition of [Margaris] p. 49. One direction, pm2.53 712, holds for all propositions, not just decidable ones. (Contributed by Jim Kingdon, 26-Mar-2018.)
Assertion
Ref Expression
dfordc (DECID 𝜑 → ((𝜑𝜓) ↔ (¬ 𝜑𝜓)))

Proof of Theorem dfordc
StepHypRef Expression
1 pm2.53 712 . 2 ((𝜑𝜓) → (¬ 𝜑𝜓))
2 pm2.54dc 877 . 2 (DECID 𝜑 → ((¬ 𝜑𝜓) → (𝜑𝜓)))
31, 2impbid2 142 1 (DECID 𝜑 → ((𝜑𝜓) ↔ (¬ 𝜑𝜓)))
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 104   ∨ wo 698  DECID wdc 820 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 604  ax-in2 605  ax-io 699 This theorem depends on definitions:  df-bi 116  df-dc 821 This theorem is referenced by:  imordc  883  pm4.64dc  886  pm5.17dc  890  pm5.6dc  912  pm3.12dc  943  pm5.15dc  1368  19.32dc  1658  r19.32vdc  2583  prime  9175  isprm4  11837  prm2orodd  11844  euclemma  11861  phiprmpw  11935
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