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Mirrors > Home > ILE Home > Th. List > ne0i | Unicode version |
Description: If a set has elements, it is not empty. A set with elements is also inhabited, see elex2 2638. (Contributed by NM, 31-Dec-1993.) |
Ref | Expression |
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ne0i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | n0i 3294 |
. 2
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2 | 1 | neneqad 2335 |
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 580 ax-in2 581 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-ne 2257 df-v 2624 df-dif 3004 df-nul 3290 |
This theorem is referenced by: ne0d 3296 ne0ii 3298 vn0 3299 inelcm 3349 rzal 3385 rexn0 3386 snnzg 3565 prnz 3570 tpnz 3573 onn0 4238 nn0eln0 4448 ordge1n0im 6216 nnmord 6292 map0g 6461 phpm 6637 fiintim 6695 addclpi 6949 mulclpi 6950 uzn0 9097 iccsupr 9447 |
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