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Theorem eldifvsn 4162
 Description: A set is an element of the universal class excluding a singleton iff it is not the singleton element. (Contributed by AV, 7-Apr-2019.)
Assertion
Ref Expression
eldifvsn

Proof of Theorem eldifvsn
StepHypRef Expression
1 elex 3118 . . 3
21biantrurd 508 . 2
3 eldifsn 4155 . 2
42, 3syl6rbbr 264 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  e.wcel 1818  =/=wne 2652   cvv 3109  \cdif 3472  {csn 4029 This theorem is referenced by:  cnvimadfsn  6927 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-ne 2654  df-v 3111  df-dif 3478  df-sn 4030
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