Theorem pm2.01i 191

Description: Inference associated with the weak Clavius law pm2.01 190. (Contributed by BJ, 30-Mar-2020.)

Hypothesis

Ref	Expression
pm2.01i.1	⊢ (𝜑 → ¬ 𝜑)

Assertion

Ref	Expression
pm2.01i	⊢ ¬ 𝜑

Proof of Theorem pm2.01i

Step	Hyp	Ref	Expression
1		pm2.01i.1	. 2 ⊢ (𝜑 → ¬ 𝜑)
2		pm2.01 190	. 2 ⊢ ((𝜑 → ¬ 𝜑) → ¬ 𝜑)
3	1, 2	ax-mp 5	1 ⊢ ¬ 𝜑

This proof depends on syntax axioms:  ¬ wn 3   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is used by:  pm2.65i  196  hfninf  37113  curryset  38037  currysetlem3  38040  quantgodel  48089  usgrexmpl12ngric  49341  usgrexmpl12ngrlic  49342