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Mirrors > Home > ILE Home > Th. List > 0ncn | Unicode version |
Description: The empty set is not a complex number. Note: do not use this after the real number axioms are developed, since it is a construction-dependent property. (Contributed by NM, 2-May-1996.) |
Ref | Expression |
---|---|
0ncn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0nelxp 4426 |
. 2
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2 | df-c 7257 |
. . 3
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3 | 2 | eleq2i 2149 |
. 2
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4 | 1, 3 | mtbir 629 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 577 ax-in2 578 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-14 1446 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 ax-sep 3922 ax-pow 3974 ax-pr 3999 |
This theorem depends on definitions: df-bi 115 df-3an 922 df-tru 1288 df-fal 1291 df-nf 1391 df-sb 1688 df-clab 2070 df-cleq 2076 df-clel 2079 df-nfc 2212 df-ne 2250 df-v 2614 df-dif 2986 df-un 2988 df-in 2990 df-ss 2997 df-nul 3270 df-pw 3408 df-sn 3428 df-pr 3429 df-op 3431 df-opab 3866 df-xp 4405 df-c 7257 |
This theorem is referenced by: (None) |
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