ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  nner Unicode version

Theorem nner 2344
Description: Negation of inequality. (Contributed by Jim Kingdon, 23-Dec-2018.)
Assertion
Ref Expression
nner  |-  ( A  =  B  ->  -.  A  =/=  B )

Proof of Theorem nner
StepHypRef Expression
1 df-ne 2341 . . 3  |-  ( A  =/=  B  <->  -.  A  =  B )
21biimpi 119 . 2  |-  ( A  =/=  B  ->  -.  A  =  B )
32con2i 622 1  |-  ( A  =  B  ->  -.  A  =/=  B )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    = wceq 1348    =/= wne 2340
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-in1 609  ax-in2 610
This theorem depends on definitions:  df-bi 116  df-ne 2341
This theorem is referenced by:  nn0eln0  4604  funtpg  5249  fin0  6863  hashnncl  10730
  Copyright terms: Public domain W3C validator