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Metamath Proof Explorer

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 ) )