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

Theorem notnoti 145
Description: Inference associated with notnot 144. (Contributed by NM, 27-Feb-2008.)
Hypothesis
Ref Expression
notnoti.1 𝜑
Assertion
Ref Expression
notnoti ¬ ¬ 𝜑

Proof of Theorem notnoti
StepHypRef Expression
1 notnoti.1 . 2 𝜑
2 notnot 144 . 2 (𝜑 → ¬ ¬ 𝜑)
31, 2ax-mp 5 1 ¬ ¬ 𝜑
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by:  nbn3  377  fal  1552  trunortruOLD  1588  trunorfalOLD  1590  ax6dgen  2133  dfnul2  4276  mdegleb  24654  nexntru  33770  amosym1  33792  ifpdfan2  40003  aisbnaxb  43346
  Copyright terms: Public domain W3C validator