Theorem bijust0 206

Description: A self-implication (see id 22) does not imply its own negation. The justification theorem bijust 207 is one of its instances. (Contributed by NM, 11-May-1999.) (Proof shortened by Josh Purinton, 29-Dec-2000.) Extract bijust0 206 from proof of bijust 207. (Revised by BJ, 19-Mar-2020.)

Assertion

Ref	Expression
bijust0	⊢ ¬ ((𝜑 → 𝜑) → ¬ (𝜑 → 𝜑))

Proof of Theorem bijust0

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ (𝜑 → 𝜑)
2		pm2.01 191	. 2 ⊢ (((𝜑 → 𝜑) → ¬ (𝜑 → 𝜑)) → ¬ (𝜑 → 𝜑))
3	1, 2	mt2 202	1 ⊢ ¬ ((𝜑 → 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:  bijust  207