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Theorem disjdif 3622
 Description: A class and its relative complement are disjoint. Theorem 38 of [Suppes] p. 29. (Contributed by NM, 24-Mar-1998.)
Assertion
Ref Expression
disjdif

Proof of Theorem disjdif
StepHypRef Expression
1 inss1 3475 . 2
2 inssdif0 3617 . 2
31, 2mpbi 199 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1642   cdif 3206   cin 3208   wss 3257  c0 3550 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-dif 3215  df-ss 3259  df-nul 3551 This theorem is referenced by:  undifv  3624  ssdifin0  3631  difdifdir  3637  sfinltfin  4535  phialllem2  4617  fvsnun1  5447  fvsnun2  5448  enadj  6060  sbthlem1  6203  dflec2  6210
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