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Theorem elirr 7312
 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 19 . . . . 5
21, 1eleq12d 2351 . . . 4
32notbid 285 . . 3
4 elirrv 7311 . . 3
53, 4vtoclg 2843 . 2
6 pm2.01 160 . 2
75, 6ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wceq 1623   wcel 1684 This theorem is referenced by:  sucprcreg  7313  alephval3  7737  exnel  24159  inttarcar  25901  bnj521  28765 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214  ax-reg 7306 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-v 2790  df-dif 3155  df-un 3157  df-nul 3456  df-sn 3646  df-pr 3647
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