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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 2746. (Contributed by NM, 31-Dec-1993.) |
Ref | Expression |
---|---|
ne0i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | n0i 3419 | . 2 | |
2 | 1 | neneqad 2419 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 2141 wne 2340 c0 3414 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ne 2341 df-v 2732 df-dif 3123 df-nul 3415 |
This theorem is referenced by: ne0d 3421 ne0ii 3423 vn0 3424 inelcm 3474 rzal 3511 rexn0 3512 snnzg 3698 prnz 3703 tpnz 3706 brne0 4036 onn0 4383 nn0eln0 4602 ordge1n0im 6412 nnmord 6493 map0g 6662 phpm 6839 fiintim 6902 addclpi 7276 mulclpi 7277 uzn0 9489 iccsupr 9910 |
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