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 → (¬ (𝜑 → 𝜓) → (¬ 𝜑 → 𝜓)))

Proof of Theorem pm2.5dc

Step	Hyp	Ref	Expression
1		pm2.5gdc 866	1 ⊢ (DECID 𝜑 → (¬ (𝜑 → 𝜓) → (¬ 𝜑 → 𝜓)))

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