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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 2676. (Contributed by NM, 31-Dec-1993.) |
Ref | Expression |
---|---|
ne0i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | n0i 3338 | . 2 | |
2 | 1 | neneqad 2364 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1465 wne 2285 c0 3333 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ne 2286 df-v 2662 df-dif 3043 df-nul 3334 |
This theorem is referenced by: ne0d 3340 ne0ii 3342 vn0 3343 inelcm 3393 rzal 3430 rexn0 3431 snnzg 3610 prnz 3615 tpnz 3618 brne0 3947 onn0 4292 nn0eln0 4503 ordge1n0im 6301 nnmord 6381 map0g 6550 phpm 6727 fiintim 6785 addclpi 7103 mulclpi 7104 uzn0 9309 iccsupr 9717 |
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