NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  nssne2 Unicode version

Theorem nssne2 3328
Description: Two classes are different if they are not subclasses of the same class. (Contributed by NM, 23-Apr-2015.)
Assertion
Ref Expression
nssne2

Proof of Theorem nssne2
StepHypRef Expression
1 sseq1 3292 . . . 4
21biimpcd 215 . . 3
32necon3bd 2553 . 2
43imp 418 1
Colors of variables: wff setvar class
Syntax hints:   wn 3   wi 4   wa 358   wceq 1642   wne 2516   wss 3257
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator