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Mirrors > Home > ILE Home > Th. List > nn0ssre | Unicode version |
Description: Nonnegative integers are a subset of the reals. (Contributed by Raph Levien, 10-Dec-2002.) |
Ref | Expression |
---|---|
nn0ssre |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-n0 8289 | . 2 | |
2 | nnssre 8043 | . . 3 | |
3 | 0re 7119 | . . . 4 | |
4 | snssi 3529 | . . . 4 | |
5 | 3, 4 | ax-mp 7 | . . 3 |
6 | 2, 5 | unssi 3147 | . 2 |
7 | 1, 6 | eqsstri 3029 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1433 cun 2971 wss 2973 csn 3398 cr 6980 cc0 6981 cn 8039 cn0 8288 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-cnex 7067 ax-resscn 7068 ax-1re 7070 ax-addrcl 7073 ax-rnegex 7085 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-sn 3404 df-int 3637 df-inn 8040 df-n0 8289 |
This theorem is referenced by: nn0sscn 8293 nn0re 8297 nn0rei 8299 nn0red 8342 |
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