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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 9483 | . 2 |
3 | 1 | rpgt0d 9486 | . 2 |
4 | 2, 3 | jca 304 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wcel 1480 class class class wbr 3929 cr 7619 cc0 7620 clt 7800 crp 9441 |
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 2121 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-rab 2425 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-sn 3533 df-pr 3534 df-op 3536 df-br 3930 df-rp 9442 |
This theorem is referenced by: reclt1d 9497 recgt1d 9498 ltrecd 9502 lerecd 9503 ltrec1d 9504 lerec2d 9505 lediv2ad 9506 ltdiv2d 9507 lediv2d 9508 ledivdivd 9509 divge0d 9524 ltmul1d 9525 ltmul2d 9526 lemul1d 9527 lemul2d 9528 ltdiv1d 9529 lediv1d 9530 ltmuldivd 9531 ltmuldiv2d 9532 lemuldivd 9533 lemuldiv2d 9534 ltdivmuld 9535 ltdivmul2d 9536 ledivmuld 9537 ledivmul2d 9538 ltdiv23d 9544 lediv23d 9545 lt2mul2divd 9552 mertenslemi1 11304 isprm6 11825 |
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