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Theorem dfor2dc 828
Description: Logical 'or' expressed in terms of implication only, for a decidable proposition. Based on theorem *5.25 of [WhiteheadRussell] p. 124. (Contributed by Jim Kingdon, 27-Mar-2018.)
Assertion
Ref Expression
dfor2dc (DECID 𝜑 → ((𝜑𝜓) ↔ ((𝜑𝜓) → 𝜓)))

Proof of Theorem dfor2dc
StepHypRef Expression
1 pm2.62 700 . 2 ((𝜑𝜓) → ((𝜑𝜓) → 𝜓))
2 pm2.68dc 827 . 2 (DECID 𝜑 → (((𝜑𝜓) → 𝜓) → (𝜑𝜓)))
31, 2impbid2 141 1 (DECID 𝜑 → ((𝜑𝜓) ↔ ((𝜑𝜓) → 𝜓)))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 103  wo 662  DECID wdc 776
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663
This theorem depends on definitions:  df-bi 115  df-dc 777
This theorem is referenced by:  imimorbdc  829
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