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Theorem pm4.81dc 878
Description: Theorem *4.81 of [WhiteheadRussell] p. 122, for decidable propositions. This one needs a decidability condition, but compare with pm4.8 681 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 825 . 2 (DECID 𝜑 → ((¬ 𝜑𝜑) → 𝜑))
2 pm2.24 595 . 2 (𝜑 → (¬ 𝜑𝜑))
31, 2impbid1 141 1 (DECID 𝜑 → ((¬ 𝜑𝜑) ↔ 𝜑))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 104  DECID wdc 804
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 588  ax-in2 589  ax-io 683
This theorem depends on definitions:  df-bi 116  df-stab 801  df-dc 805
This theorem is referenced by: (None)
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