Theorem elirrv 4614

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	|- -. x e. x

Proof of Theorem elirrv

Step	Hyp	Ref	Expression
1		elirr 4607	1 |- -. x e. x

Syntax hints:   -. wn 3

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189  ax-setind 4603

This theorem depends on definitions:  df-bi 117  df-3an 983  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-nfc 2339  df-ne 2379  df-ral 2491  df-v 2778  df-dif 3176  df-sn 3649

This theorem is referenced by:  ruv  4616  dtruex  4625  tfrlemisucfn  6433  tfrlemisucaccv  6434  ltsopi  7468