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Mirrors > Home > ILE Home > Th. List > nn0sscn | GIF version |
Description: Nonnegative integers are a subset of the complex numbers.) (Contributed by NM, 9-May-2004.) |
Ref | Expression |
---|---|
nn0sscn | ⊢ ℕ0 ⊆ ℂ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nn0ssre 8185 | . 2 ⊢ ℕ0 ⊆ ℝ | |
2 | ax-resscn 6976 | . 2 ⊢ ℝ ⊆ ℂ | |
3 | 1, 2 | sstri 2954 | 1 ⊢ ℕ0 ⊆ ℂ |
Colors of variables: wff set class |
Syntax hints: ⊆ wss 2917 ℂcc 6887 ℝcr 6888 ℕ0cn0 8181 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-cnex 6975 ax-resscn 6976 ax-1re 6978 ax-addrcl 6981 ax-rnegex 6993 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-sn 3381 df-int 3616 df-inn 7915 df-n0 8182 |
This theorem is referenced by: nn0cn 8191 nn0expcl 9269 |
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