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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 3427. (Contributed by Glauco Siliprandi, 11-Dec-2019.) |
Ref | Expression |
---|---|
n0ii.1 |
Ref | Expression |
---|---|
ne0ii |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | n0ii.1 | . 2 | |
2 | ne0i 3427 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2146 wne 2345 c0 3420 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1445 ax-7 1446 ax-gen 1447 ax-ie1 1491 ax-ie2 1492 ax-8 1502 ax-10 1503 ax-11 1504 ax-i12 1505 ax-bndl 1507 ax-4 1508 ax-17 1524 ax-i9 1528 ax-ial 1532 ax-i5r 1533 ax-ext 2157 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1459 df-sb 1761 df-clab 2162 df-cleq 2168 df-clel 2171 df-nfc 2306 df-ne 2346 df-v 2737 df-dif 3129 df-nul 3421 |
This theorem is referenced by: pw1ne0 7217 sucpw1nel3 7222 |
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