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Theorem pm4.81dc 825
Description: Theorem *4.81 of [WhiteheadRussell] p. 122, for decidable propositions. This one needs a decidability condition, but compare with pm4.8 633 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 761 . 2 (DECID 𝜑 → ((¬ 𝜑𝜑) → 𝜑))
2 pm2.24 561 . 2 (𝜑 → (¬ 𝜑𝜑))
31, 2impbid1 134 1 (DECID 𝜑 → ((¬ 𝜑𝜑) ↔ 𝜑))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 102  DECID wdc 753
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in2 555  ax-io 640
This theorem depends on definitions:  df-bi 114  df-dc 754
This theorem is referenced by: (None)
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