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Mirrors > Home > MPE Home > Th. List > elirr | Structured version Visualization version Unicode version |
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.) |
Ref | Expression |
---|---|
elirr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 22 |
. . . . 5
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2 | 1, 1 | eleq12d 2525 |
. . . 4
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3 | 2 | notbid 296 |
. . 3
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4 | elirrv 8117 |
. . 3
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5 | 3, 4 | vtoclg 3109 |
. 2
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6 | pm2.01 172 |
. 2
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7 | 5, 6 | ax-mp 5 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() |
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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