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Mirrors > Home > ILE Home > Th. List > nn0rei | GIF version |
Description: A nonnegative integer is a real number. (Contributed by NM, 14-May-2003.) |
Ref | Expression |
---|---|
nn0re.1 | ⊢ 𝐴 ∈ ℕ0 |
Ref | Expression |
---|---|
nn0rei | ⊢ 𝐴 ∈ ℝ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nn0ssre 8292 | . 2 ⊢ ℕ0 ⊆ ℝ | |
2 | nn0re.1 | . 2 ⊢ 𝐴 ∈ ℕ0 | |
3 | 1, 2 | sselii 2996 | 1 ⊢ 𝐴 ∈ ℝ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1433 ℝcr 6980 ℕ0cn0 8288 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-cnex 7067 ax-resscn 7068 ax-1re 7070 ax-addrcl 7073 ax-rnegex 7085 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-sn 3404 df-int 3637 df-inn 8040 df-n0 8289 |
This theorem is referenced by: nn0cni 8300 nn0le2xi 8338 nn0lele2xi 8339 numlt 8501 numltc 8502 decle 8510 decleh 8511 |
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