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Theorem disj1 3869
 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 3867 . 2
2 df-ral 2812 . 2
31, 2bitri 249 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  <->wb 184  A.wal 1393  =wceq 1395  e.wcel 1818  A.wral 2807  i^icin 3474   c0 3784 This theorem is referenced by:  reldisj  3870  disj3  3871  undif4  3883  disjsn  4090  funun  5635  zfregs2  8185  dfac5lem4  8528  isf32lem9  8762  fzodisj  11859  zfregs2VD  33641  bnj1280  34076 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-v 3111  df-dif 3478  df-in 3482  df-nul 3785
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