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Mirrors > Home > ILE Home > Th. List > nncni | GIF version |
Description: A positive integer is a complex number. (Contributed by NM, 18-Aug-1999.) |
Ref | Expression |
---|---|
nnre.1 | ⊢ 𝐴 ∈ ℕ |
Ref | Expression |
---|---|
nncni | ⊢ 𝐴 ∈ ℂ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnre.1 | . . 3 ⊢ 𝐴 ∈ ℕ | |
2 | 1 | nnrei 8722 | . 2 ⊢ 𝐴 ∈ ℝ |
3 | 2 | recni 7771 | 1 ⊢ 𝐴 ∈ ℂ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1480 ℂcc 7611 ℕcn 8713 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-cnex 7704 ax-resscn 7705 ax-1re 7707 ax-addrcl 7710 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-v 2683 df-in 3072 df-ss 3079 df-int 3767 df-inn 8714 |
This theorem is referenced by: 9p1e10 9177 numnncl2 9197 dec10p 9217 3dec 10454 4bc2eq6 10513 ef01bndlem 11452 |
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