Theorem bj-nimn 34744

Description: If a formula is true, then it does not imply its negation. (Contributed by BJ, 19-Mar-2020.) A shorter proof is possible using id 22 and jc 161, however, the present proof uses theorems that are more basic than jc 161. (Proof modification is discouraged.)

Assertion

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

Proof of Theorem bj-nimn

Step	Hyp	Ref	Expression
1		pm2.01 188	. 2 ⊢ ((𝜑 → ¬ 𝜑) → ¬ 𝜑)
2	1	con2i 139	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:  bj-nimni  34745