Theorem pm2.521dcALT 855

Description: Alternate proof of pm2.521dc 854. (Contributed by Jim Kingdon, 5-May-2018.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

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

Proof of Theorem pm2.521dcALT

Step	Hyp	Ref	Expression
1		pm2.52 645	. 2 ⊢ (¬ (𝜑 → 𝜓) → (¬ 𝜑 → ¬ 𝜓))
2		condc 838	. 2 ⊢ (DECID 𝜑 → ((¬ 𝜑 → ¬ 𝜓) → (𝜓 → 𝜑)))
3	1, 2	syl5 32	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)