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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 2755. (Contributed by NM, 31-Dec-1993.) |
Ref | Expression |
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ne0i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | n0i 3430 |
. 2
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2 | 1 | neneqad 2426 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
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 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-v 2741 df-dif 3133 df-nul 3425 |
This theorem is referenced by: ne0d 3432 ne0ii 3434 vn0 3435 inelcm 3485 rzal 3522 rexn0 3523 snnzg 3711 prnz 3716 tpnz 3719 brne0 4054 onn0 4402 nn0eln0 4621 ordge1n0im 6440 nnmord 6521 map0g 6691 phpm 6868 fiintim 6931 addclpi 7329 mulclpi 7330 uzn0 9546 iccsupr 9969 ringn0 13243 |
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