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Theorem pm4.64dc 900
Description: Theorem *4.64 of [WhiteheadRussell] p. 120, given a decidability condition. The reverse direction, pm2.53 722, 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 892 . 2 (DECID 𝜑 → ((𝜑𝜓) ↔ (¬ 𝜑𝜓)))
21bicomd 141 1 (DECID 𝜑 → ((¬ 𝜑𝜓) ↔ (𝜑𝜓)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 105  wo 708  DECID wdc 834
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-io 709
This theorem depends on definitions:  df-bi 117  df-dc 835
This theorem is referenced by:  pm4.66dc  901
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