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	$$⊢\neg \left(\left(\phi \to \phi \right)\to \neg \left(\phi \to \phi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢\phi \to \phi$$
2		pm2.01	$$⊢\left(\left(\phi \to \phi \right)\to \neg \left(\phi \to \phi \right)\right)\to \neg \left(\phi \to \phi \right)$$
3	1 2	mt2	$$⊢\neg \left(\left(\phi \to \phi \right)\to \neg \left(\phi \to \phi \right)\right)$$