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Mirrors > Home > ILE Home > Th. List > nnred | Unicode version |
Description: A positive integer is a real number. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
nnred.1 |
Ref | Expression |
---|---|
nnred |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnssre 7918 | . 2 | |
2 | nnred.1 | . 2 | |
3 | 1, 2 | sseldi 2943 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1393 cr 6888 cn 7914 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-cnex 6975 ax-resscn 6976 ax-1re 6978 ax-addrcl 6981 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-v 2559 df-in 2924 df-ss 2931 df-int 3616 df-inn 7915 |
This theorem is referenced by: qbtwnzlemstep 9103 qbtwnrelemcalc 9110 qbtwnre 9111 flqdiv 9163 modqmulnn 9184 bernneq3 9371 expnbnd 9372 caucvgrelemcau 9579 caucvgre 9580 cvg1nlemcxze 9581 cvg1nlemcau 9583 cvg1nlemres 9584 resqrexlemdecn 9610 resqrexlemga 9621 |
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