MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  bijust0 Structured version   Visualization version   GIF version

Theorem bijust0 207
Description: A self-implication (see id 22) does not imply its own negation. The justification theorem bijust 208 is one of its instances. (Contributed by NM, 11-May-1999.) (Proof shortened by Josh Purinton, 29-Dec-2000.) Extract bijust0 207 from proof of bijust 208. (Revised by BJ, 19-Mar-2020.)
Assertion
Ref Expression
bijust0 ¬ ((𝜑𝜑) → ¬ (𝜑𝜑))

Proof of Theorem bijust0
StepHypRef Expression
1 id 22 . 2 (𝜑𝜑)
2 pm2.01 192 . 2 (((𝜑𝜑) → ¬ (𝜑𝜑)) → ¬ (𝜑𝜑))
31, 2mt2 203 1 ¬ ((𝜑𝜑) → ¬ (𝜑𝜑))
Colors of variables: wff setvar class
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  208
  Copyright terms: Public domain W3C validator