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Mirrors > Home > ILE Home > Th. List > ne0ii | Unicode version |
Description: If a class has elements, then it is nonempty. Inference associated with ne0i 3333. (Contributed by Glauco Siliprandi, 11-Dec-2019.) |
Ref | Expression |
---|---|
n0ii.1 |
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Ref | Expression |
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ne0ii |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | n0ii.1 |
. 2
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2 | ne0i 3333 |
. 2
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3 | 1, 2 | ax-mp 7 |
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 105 ax-ia2 106 ax-ia3 107 ax-in1 586 ax-in2 587 ax-io 681 ax-5 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 |
This theorem depends on definitions: df-bi 116 df-tru 1315 df-nf 1418 df-sb 1717 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-ne 2281 df-v 2657 df-dif 3037 df-nul 3328 |
This theorem is referenced by: (None) |
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