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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 8974 | . 2 ⊢ ℕ0 ⊆ ℝ | |
2 | nn0re.1 | . 2 ⊢ 𝐴 ∈ ℕ0 | |
3 | 1, 2 | sselii 3089 | 1 ⊢ 𝐴 ∈ ℝ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1480 ℝcr 7612 ℕ0cn0 8970 |
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 ax-rnegex 7722 |
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-rex 2420 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-sn 3528 df-int 3767 df-inn 8714 df-n0 8971 |
This theorem is referenced by: nn0cni 8982 nn0le2xi 9020 nn0lele2xi 9021 numlt 9199 numltc 9200 decle 9208 decleh 9209 |
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