![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > zcn | GIF version |
Description: An integer is a complex number. (Contributed by NM, 9-May-2004.) |
Ref | Expression |
---|---|
zcn | ⊢ (𝑁 ∈ ℤ → 𝑁 ∈ ℂ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | zre 8025 | . 2 ⊢ (𝑁 ∈ ℤ → 𝑁 ∈ ℝ) | |
2 | 1 | recnd 6851 | 1 ⊢ (𝑁 ∈ ℤ → 𝑁 ∈ ℂ) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∈ wcel 1390 ℂcc 6709 ℤcz 8021 |
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 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 ax-resscn 6775 |
This theorem depends on definitions: df-bi 110 df-3or 885 df-3an 886 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-rex 2306 df-rab 2309 df-v 2553 df-un 2916 df-in 2918 df-ss 2925 df-sn 3373 df-pr 3374 df-op 3376 df-uni 3572 df-br 3756 df-iota 4810 df-fv 4853 df-ov 5458 df-neg 6982 df-z 8022 |
This theorem is referenced by: zsscn 8029 zaddcllempos 8058 peano2zm 8059 zaddcllemneg 8060 zaddcl 8061 zsubcl 8062 zrevaddcl 8071 zlem1lt 8076 zltlem1 8077 zapne 8091 zdiv 8104 zdivadd 8105 zdivmul 8106 zextlt 8108 zneo 8115 zeo2 8120 peano5uzti 8122 zindd 8132 divfnzn 8332 qmulz 8334 zq 8337 qaddcl 8346 qnegcl 8347 qmulcl 8348 qreccl 8351 fzen 8677 uzsubsubfz 8681 fz01en 8687 fzmmmeqm 8691 fzsubel 8693 fztp 8710 fzsuc2 8711 fzrev2 8717 fzrev3 8719 elfzp1b 8729 fzrevral 8737 fzrevral2 8738 fzrevral3 8739 fzshftral 8740 fzoaddel2 8819 fzosubel2 8821 eluzgtdifelfzo 8823 fzocatel 8825 elfzom1elp1fzo 8828 fzval3 8830 zpnn0elfzo1 8834 fzosplitprm1 8860 fzoshftral 8864 frecfzen2 8885 expsubap 8956 zesq 9020 |
Copyright terms: Public domain | W3C validator |