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Theorem elirr 8118
 Description: No class is a member of itself. Exercise 6 of [TakeutiZaring] p. 22. (Contributed by NM, 7-Aug-1994.) (Proof shortened by Andrew Salmon, 9-Jul-2011.)
Assertion
Ref Expression
elirr

Proof of Theorem elirr
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 id 22 . . . . 5
21, 1eleq12d 2525 . . . 4
32notbid 296 . . 3
4 elirrv 8117 . . 3
53, 4vtoclg 3109 . 2
6 pm2.01 172 . 2
75, 6ax-mp 5 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wceq 1446   wcel 1889 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1671  ax-4 1684  ax-5 1760  ax-6 1807  ax-7 1853  ax-9 1898  ax-10 1917  ax-11 1922  ax-12 1935  ax-13 2093  ax-ext 2433  ax-sep 4528  ax-nul 4537  ax-pr 4642  ax-reg 8112 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1449  df-ex 1666  df-nf 1670  df-sb 1800  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2583  df-ne 2626  df-ral 2744  df-rex 2745  df-v 3049  df-dif 3409  df-un 3411  df-nul 3734  df-sn 3971  df-pr 3973 This theorem is referenced by:  sucprcreg  8119  alephval3  8546  bnj521  29557  rankeq1o  30950  hfninf  30965  bj-disjcsn  31554
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