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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 8949 | . 2 ⊢ ℕ0 ⊆ ℝ | |
2 | nn0re.1 | . 2 ⊢ 𝐴 ∈ ℕ0 | |
3 | 1, 2 | sselii 3064 | 1 ⊢ 𝐴 ∈ ℝ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1465 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: nn0cni 8957 nn0le2xi 8995 nn0lele2xi 8996 numlt 9174 numltc 9175 decle 9183 decleh 9184 |
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