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Theorem pm4.64dc 800
Description: Theorem *4.64 of [WhiteheadRussell] p. 120, given a decidability condition. The reverse direction, pm2.53 640, holds for all propositions. (Contributed by Jim Kingdon, 2-May-2018.)
Assertion
Ref Expression
pm4.64dc (DECID φ → ((¬ φψ) ↔ (φ ψ)))

Proof of Theorem pm4.64dc
StepHypRef Expression
1 dfordc 790 . 2 (DECID φ → ((φ ψ) ↔ (¬ φψ)))
21bicomd 129 1 (DECID φ → ((¬ φψ) ↔ (φ ψ)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 98   wo 628  DECID wdc 741
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 629
This theorem depends on definitions:  df-bi 110  df-dc 742
This theorem is referenced by:  pm4.66dc  801
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