Theorem elirrv 4532

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 ∈ 𝑥

Proof of Theorem elirrv

Step	Hyp	Ref	Expression
1		elirr 4525	1 ⊢ ¬ 𝑥 ∈ 𝑥

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 609  ax-in2 610  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152  ax-setind 4521

This theorem depends on definitions:  df-bi 116  df-3an 975  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-ne 2341  df-ral 2453  df-v 2732  df-dif 3123  df-sn 3589

This theorem is referenced by:  ruv  4534  dtruex  4543  tfrlemisucfn  6303  tfrlemisucaccv  6304  ltsopi  7282