MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ne3anior Unicode version

Theorem ne3anior 2783
Description: A De Morgan's law for inequality. (Contributed by NM, 30-Sep-2013.)
Assertion
Ref Expression
ne3anior

Proof of Theorem ne3anior
StepHypRef Expression
1 3anor 989 . 2
2 nne 2658 . . 3
3 nne 2658 . . 3
4 nne 2658 . . 3
52, 3, 43orbi123i 1186 . 2
61, 5xchbinx 310 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  <->wb 184  \/w3o 972  /\w3a 973  =wceq 1395  =/=wne 2652
This theorem is referenced by:  eldiftp  4072
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 974  df-3an 975  df-ne 2654
  Copyright terms: Public domain W3C validator