Theorem bj-nnclavius 13772

Description: Clavius law with doubly negated consequent. (Contributed by BJ, 4-Dec-2023.)

Assertion

Ref	Expression
bj-nnclavius	⊢ ((¬ 𝜑 → 𝜑) → ¬ ¬ 𝜑)

Proof of Theorem bj-nnclavius

Step	Hyp	Ref	Expression
1		con3 637	. 2 ⊢ ((¬ 𝜑 → 𝜑) → (¬ 𝜑 → ¬ ¬ 𝜑))
2	1	pm2.01d 613	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-in1 609  ax-in2 610

This theorem is referenced by:  bj-pm2.18st  13785