Theorem bijust0

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

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

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( 𝜑 → 𝜑 )
2		pm2.01	⊢ ( ( ( 𝜑 → 𝜑 ) → ¬ ( 𝜑 → 𝜑 ) ) → ¬ ( 𝜑 → 𝜑 ) )
3	1 2	mt2	⊢ ¬ ( ( 𝜑 → 𝜑 ) → ¬ ( 𝜑 → 𝜑 ) )