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Theorem pm4.81dc 813
Description: Theorem *4.81 of [WhiteheadRussell] p. 122, for decidable propositions. This one needs a decidability condition, but compare with pm4.8 622 which holds for all propositions. (Contributed by Jim Kingdon, 4-Jul-2018.)
Assertion
Ref Expression
pm4.81dc (DECID φ → ((¬ φφ) ↔ φ))

Proof of Theorem pm4.81dc
StepHypRef Expression
1 pm2.18dc 749 . 2 (DECID φ → ((¬ φφ) → φ))
2 pm2.24 551 . 2 (φ → (¬ φφ))
31, 2impbid1 130 1 (DECID φ → ((¬ φφ) ↔ φ))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 98  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-in2 545  ax-io 629
This theorem depends on definitions:  df-bi 110  df-dc 742
This theorem is referenced by: (None)
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