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Mirrors > Home > ILE Home > Th. List > nn0ssre | Unicode version |
Description: Nonnegative integers are a subset of the reals. (Contributed by Raph Levien, 10-Dec-2002.) |
Ref | Expression |
---|---|
nn0ssre |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-n0 8971 | . 2 | |
2 | nnssre 8717 | . . 3 | |
3 | 0re 7759 | . . . 4 | |
4 | snssi 3659 | . . . 4 | |
5 | 3, 4 | ax-mp 5 | . . 3 |
6 | 2, 5 | unssi 3246 | . 2 |
7 | 1, 6 | eqsstri 3124 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1480 cun 3064 wss 3066 csn 3522 cr 7612 cc0 7613 cn 8713 cn0 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: nn0sscn 8975 nn0re 8979 nn0rei 8981 nn0red 9024 |
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