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	|- -. ( ( ph -> ph ) -> -. ( ph -> ph ) )

Proof

Step	Hyp	Ref	Expression
1		id	|- ( ph -> ph )
2		pm2.01	|- ( ( ( ph -> ph ) -> -. ( ph -> ph ) ) -> -. ( ph -> ph ) )
3	1 2	mt2	|- -. ( ( ph -> ph ) -> -. ( ph -> ph ) )