Theorem pm2.521dc 854

Description: Theorem *2.521 of [WhiteheadRussell] p. 107, but with an additional decidability condition. Note that by replacing in proof pm2.52 645 with conax1k 643, we obtain a proof of the more general instance where the last occurrence of 𝜑 is replaced with any 𝜒. (Contributed by Jim Kingdon, 5-May-2018.)

Assertion

Ref	Expression
pm2.521dc	⊢ (DECID 𝜑 → (¬ (𝜑 → 𝜓) → (𝜓 → 𝜑)))

Proof of Theorem pm2.521dc

Step	Hyp	Ref	Expression
1		pm2.521gdc 853	1 ⊢ (DECID 𝜑 → (¬ (𝜑 → 𝜓) → (𝜓 → 𝜑)))

Syntax hints:  ¬ wn 3   → wi 4  DECID wdc 819

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 603  ax-in2 604  ax-io 698

This theorem depends on definitions:  df-bi 116  df-stab 816  df-dc 820

This theorem is referenced by: (None)