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Theorem disj1 3408
 Description: Two ways of saying that two classes are disjoint (have no members in common). (Contributed by NM, 19-Aug-1993.)
Assertion
Ref Expression
disj1
Distinct variable groups:   ,   ,

Proof of Theorem disj1
StepHypRef Expression
1 disj 3406 . 2
2 df-ral 2419 . 2
31, 2bitri 183 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 104  wal 1329   wceq 1331   wcel 1480  wral 2414   cin 3065  c0 3358 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-ral 2419  df-v 2683  df-dif 3068  df-in 3072  df-nul 3359 This theorem is referenced by:  reldisj  3409  disj3  3410  undif4  3420  disjsn  3580  funun  5162  fzodisj  9948
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