Theorem pm2.18i 129

Description: Inference associated with the Clavius law pm2.18 128. (Contributed by BJ, 30-Mar-2020.)

Hypothesis

Ref	Expression
pm2.18i.1	⊢ (¬ 𝜑 → 𝜑)

Assertion

Ref	Expression
pm2.18i	⊢ 𝜑

Proof of Theorem pm2.18i

Step	Hyp	Ref	Expression
1		pm2.18i.1	. 2 ⊢ (¬ 𝜑 → 𝜑)
2		pm2.18 128	. 2 ⊢ ((¬ 𝜑 → 𝜑) → 𝜑)
3	1, 2	ax-mp 5	1 ⊢ 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:  notnotriALT  132  pm2.61i  182  sn-00id  42411  3cubes  42680