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Mirrors > Home > ILE Home > Th. List > rpregt0d | Unicode version |
Description: A positive real is real and greater than zero. (Contributed by Mario Carneiro, 28-May-2016.) |
Ref | Expression |
---|---|
rpred.1 |
Ref | Expression |
---|---|
rpregt0d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rpred.1 | . . 3 | |
2 | 1 | rpred 9451 | . 2 |
3 | 1 | rpgt0d 9454 | . 2 |
4 | 2, 3 | jca 304 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wcel 1465 class class class wbr 3899 cr 7587 cc0 7588 clt 7768 crp 9409 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-rab 2402 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 df-rp 9410 |
This theorem is referenced by: reclt1d 9465 recgt1d 9466 ltrecd 9470 lerecd 9471 ltrec1d 9472 lerec2d 9473 lediv2ad 9474 ltdiv2d 9475 lediv2d 9476 ledivdivd 9477 divge0d 9492 ltmul1d 9493 ltmul2d 9494 lemul1d 9495 lemul2d 9496 ltdiv1d 9497 lediv1d 9498 ltmuldivd 9499 ltmuldiv2d 9500 lemuldivd 9501 lemuldiv2d 9502 ltdivmuld 9503 ltdivmul2d 9504 ledivmuld 9505 ledivmul2d 9506 ltdiv23d 9512 lediv23d 9513 lt2mul2divd 9520 mertenslemi1 11272 isprm6 11752 |
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