Theorem pm2.18OLD 129

Description: Obsolete version of pm2.18 128 as of 17-Nov-2023. (Contributed by NM, 29-Dec-1992.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
pm2.18OLD	⊢ ((¬ 𝜑 → 𝜑) → 𝜑)

Proof of Theorem pm2.18OLD

Step	Hyp	Ref	Expression
1		pm2.21 123	. . . 4 ⊢ (¬ 𝜑 → (𝜑 → ¬ (¬ 𝜑 → 𝜑)))
2	1	a2i 14	. . 3 ⊢ ((¬ 𝜑 → 𝜑) → (¬ 𝜑 → ¬ (¬ 𝜑 → 𝜑)))
3	2	con4d 115	. 2 ⊢ ((¬ 𝜑 → 𝜑) → ((¬ 𝜑 → 𝜑) → 𝜑))
4	3	pm2.43i 52	1 ⊢ ((¬ 𝜑 → 𝜑) → 𝜑)

Syntax hints:  ¬ wn 3   → wi 4

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

This theorem is referenced by:  pm2.18dOLD  130