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Theorem eldifvsn 4147
 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 3104 . . 3
21biantrurd 508 . 2
3 eldifsn 4140 . 2
42, 3syl6rbbr 264 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   wcel 1804   wne 2638  cvv 3095   cdif 3458  csn 4014 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-ne 2640  df-v 3097  df-dif 3464  df-sn 4015 This theorem is referenced by:  cnvimadfsn  6912
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