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Theorem dfordc 791
 Description: Definition of 'or' in terms of negation and implication for a decidable proposition. Based on definition of [Margaris] p. 49. One direction, pm2.53 641, 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 pm2.53 641 . 2 ((𝜑𝜓) → (¬ 𝜑𝜓))
2 pm2.54dc 790 . 2 (DECID 𝜑 → ((¬ 𝜑𝜓) → (𝜑𝜓)))
31, 2impbid2 131 1 (DECID 𝜑 → ((𝜑𝜓) ↔ (¬ 𝜑𝜓)))
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 98   ∨ wo 629  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-in1 544  ax-in2 545  ax-io 630 This theorem depends on definitions:  df-bi 110  df-dc 743 This theorem is referenced by:  imordc  796  pm4.64dc  801  pm5.17dc  810  pm5.6dc  835  pm3.12dc  865  pm5.15dc  1280  19.32dc  1569  r19.32vdc  2459  prime  8337
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