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Theorem nelne1 2548
 Description: Two classes are different if they don't contain the same element. (Contributed by NM, 3-Feb-2012.)
Assertion
Ref Expression
nelne1

Proof of Theorem nelne1
StepHypRef Expression
1 eleq2 2357 . . . 4
21biimpcd 215 . . 3
32necon3bd 2496 . 2
43imp 418 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 358   wceq 1632   wcel 1696   wne 2459 This theorem is referenced by:  difsnb  3773  fofinf1o  7153  fin23lem24  7964  fin23lem31  7985  ttukeylem7  8158  canth4  8285  npomex  8636  lbspss  15851  islbs3  15924  lbsextlem4  15930  obslbs  16646  hauspwpwf1  17698  ppiltx  20431  ex-pss  20831  cntnevol  23191  lppotos  26247  rpnnen3lem  27227  lshpnelb  29796  osumcllem10N  30776  pexmidlem7N  30787  dochsnkrlem1  32281 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-11 1727  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-cleq 2289  df-clel 2292  df-ne 2461
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