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Theorem elirrv 4300
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 4294 1 ¬ 𝑥𝑥
Colors of variables: wff set class
Syntax hints:  ¬ wn 3
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-setind 4290
This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ne 2221  df-ral 2328  df-v 2576  df-dif 2948  df-sn 3409
This theorem is referenced by:  ruv  4302  tfrlemisucfn  5969  tfrlemisucaccv  5970  ltsopi  6476
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