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Theorem elirrv 4458
 Description: The membership relation is irreflexive: no set is a member of itself. Theorem 105 of [Suppes] p. 54. (Contributed by NM, 19-Aug-1993.)
Assertion
Ref Expression
elirrv ¬ 𝑥𝑥

Proof of Theorem elirrv
StepHypRef Expression
1 elirr 4451 1 ¬ 𝑥𝑥
 Colors of variables: wff set class Syntax hints:  ¬ wn 3 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  ax-setind 4447 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-ne 2307  df-ral 2419  df-v 2683  df-dif 3068  df-sn 3528 This theorem is referenced by:  ruv  4460  dtruex  4469  tfrlemisucfn  6214  tfrlemisucaccv  6215  ltsopi  7121
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