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Theorem disj1 3672
 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 3670 . 2
2 df-ral 2712 . 2
31, 2bitri 242 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178  wal 1550   wceq 1653   wcel 1726  wral 2707   cin 3321  c0 3630 This theorem is referenced by:  reldisj  3673  disj3  3674  undif4  3686  disjsn  3870  funun  5497  zfregs2  7671  dfac5lem4  8009  isf32lem9  8243  fzodisj  11169  zfregs2VD  29015  bnj1280  29451 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-v 2960  df-dif 3325  df-in 3329  df-nul 3631
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