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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 8949 | . 2 ⊢ ℕ0 ⊆ ℝ | |
2 | ax-resscn 7680 | . 2 ⊢ ℝ ⊆ ℂ | |
3 | 1, 2 | sstri 3076 | 1 ⊢ ℕ0 ⊆ ℂ |
Colors of variables: wff set class |
Syntax hints: ⊆ wss 3041 ℂcc 7586 ℝcr 7587 ℕ0cn0 8945 |
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-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 ax-sep 4016 ax-cnex 7679 ax-resscn 7680 ax-1re 7682 ax-addrcl 7685 ax-rnegex 7697 |
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-ral 2398 df-rex 2399 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-sn 3503 df-int 3742 df-inn 8689 df-n0 8946 |
This theorem is referenced by: nn0cn 8955 nn0expcl 10275 fsumnn0cl 11140 |
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