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Theorem pm2.5dc 867
Description: Negating an implication for a decidable antecedent. Theorem *2.5 of [WhiteheadRussell] p. 107 under a decidability condition. (Contributed by Jim Kingdon, 29-Mar-2018.)
Assertion
Ref Expression
pm2.5dc (DECID 𝜑 → (¬ (𝜑𝜓) → (¬ 𝜑𝜓)))

Proof of Theorem pm2.5dc
StepHypRef Expression
1 pm2.5gdc 866 1 (DECID 𝜑 → (¬ (𝜑𝜓) → (¬ 𝜑𝜓)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  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-stab 831  df-dc 835
This theorem is referenced by:  pm5.11dc  909
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