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Mirrors > Home > ILE Home > Th. List > rpgecld | Unicode version |
Description: A number greater or equal to a positive real is positive real. (Contributed by Mario Carneiro, 28-May-2016.) |
Ref | Expression |
---|---|
rpgecld.1 |
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rpgecld.2 |
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rpgecld.3 |
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Ref | Expression |
---|---|
rpgecld |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rpgecld.2 |
. 2
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2 | rpgecld.1 |
. 2
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3 | rpgecld.3 |
. 2
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4 | rpgecl 9225 |
. 2
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5 | 1, 2, 3, 4 | syl3anc 1175 |
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-in1 580 ax-in2 581 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-13 1450 ax-14 1451 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-sep 3965 ax-pow 4017 ax-pr 4047 ax-un 4271 ax-setind 4368 ax-cnex 7499 ax-resscn 7500 ax-1re 7502 ax-addrcl 7505 ax-rnegex 7517 ax-pre-ltwlin 7521 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-fal 1296 df-nf 1396 df-sb 1694 df-eu 1952 df-mo 1953 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-ne 2257 df-nel 2352 df-ral 2365 df-rex 2366 df-rab 2369 df-v 2624 df-dif 3004 df-un 3006 df-in 3008 df-ss 3015 df-pw 3437 df-sn 3458 df-pr 3459 df-op 3461 df-uni 3662 df-br 3854 df-opab 3908 df-xp 4460 df-cnv 4462 df-pnf 7587 df-mnf 7588 df-xr 7589 df-ltxr 7590 df-le 7591 df-rp 9198 |
This theorem is referenced by: isumrpcl 10951 |
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