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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 8731 | . 2 ⊢ ℕ0 ⊆ ℝ | |
2 | ax-resscn 7491 | . 2 ⊢ ℝ ⊆ ℂ | |
3 | 1, 2 | sstri 3035 | 1 ⊢ ℕ0 ⊆ ℂ |
Colors of variables: wff set class |
Syntax hints: ⊆ wss 3000 ℂcc 7402 ℝcr 7403 ℕ0cn0 8727 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-sep 3963 ax-cnex 7490 ax-resscn 7491 ax-1re 7493 ax-addrcl 7496 ax-rnegex 7508 |
This theorem depends on definitions: df-bi 116 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-ral 2365 df-rex 2366 df-v 2622 df-un 3004 df-in 3006 df-ss 3013 df-sn 3456 df-int 3695 df-inn 8477 df-n0 8728 |
This theorem is referenced by: nn0cn 8737 nn0expcl 10023 fsumnn0cl 10851 |
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