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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-n0 8735 |
. 2
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2 | nnssre 8487 |
. . 3
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3 | 0re 7549 |
. . . 4
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4 | snssi 3587 |
. . . 4
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5 | 3, 4 | ax-mp 7 |
. . 3
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6 | 2, 5 | unssi 3176 |
. 2
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7 | 1, 6 | eqsstri 3057 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-sep 3963 ax-cnex 7497 ax-resscn 7498 ax-1re 7500 ax-addrcl 7503 ax-rnegex 7515 |
This theorem depends on definitions: df-bi 116 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-ral 2365 df-rex 2366 df-v 2622 df-un 3004 df-in 3006 df-ss 3013 df-sn 3456 df-int 3695 df-inn 8484 df-n0 8735 |
This theorem is referenced by: nn0sscn 8739 nn0re 8743 nn0rei 8745 nn0red 8788 |
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