Theorem pm4.81ALT 32546

Description: Alternate proof of pm4.81 381. (Contributed by BJ, 30-Mar-2020.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
pm4.81ALT	⊢ ((¬ 𝜑 → 𝜑) ↔ 𝜑)

Proof of Theorem pm4.81ALT

Step	Hyp	Ref	Expression
1		pm2.18 122	. 2 ⊢ ((¬ 𝜑 → 𝜑) → 𝜑)
2		ax-1 6	. 2 ⊢ (𝜑 → (¬ 𝜑 → 𝜑))
3	1, 2	impbii 199	1 ⊢ ((¬ 𝜑 → 𝜑) ↔ 𝜑)

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 196

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197

This theorem is referenced by: (None)