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

Theorem neir 2309
Description: Inference associated with df-ne 2307. (Contributed by BJ, 7-Jul-2018.)
Hypothesis
Ref Expression
neir.1  |-  -.  A  =  B
Assertion
Ref Expression
neir  |-  A  =/= 
B

Proof of Theorem neir
StepHypRef Expression
1 neir.1 . 2  |-  -.  A  =  B
2 df-ne 2307 . 2  |-  ( A  =/=  B  <->  -.  A  =  B )
31, 2mpbir 145 1  |-  A  =/= 
B
Colors of variables: wff set class
Syntax hints:   -. wn 3    = wceq 1331    =/= wne 2306
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-ne 2307
This theorem is referenced by:  exmidonfinlem  7042  ine0  8149  pwle2  13182
  Copyright terms: Public domain W3C validator