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Theorem pm4.64dc 837
Description: Theorem *4.64 of [WhiteheadRussell] p. 120, given a decidability condition. The reverse direction, pm2.53 674, holds for all propositions. (Contributed by Jim Kingdon, 2-May-2018.)
Assertion
Ref Expression
pm4.64dc (DECID 𝜑 → ((¬ 𝜑𝜓) ↔ (𝜑𝜓)))

Proof of Theorem pm4.64dc
StepHypRef Expression
1 dfordc 827 . 2 (DECID 𝜑 → ((𝜑𝜓) ↔ (¬ 𝜑𝜓)))
21bicomd 139 1 (DECID 𝜑 → ((¬ 𝜑𝜓) ↔ (𝜑𝜓)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 103  wo 662  DECID wdc 778
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 779
This theorem is referenced by:  pm4.66dc  838
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