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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 |
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Ref | Expression |
---|---|
rpregt0d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rpred.1 |
. . 3
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2 | 1 | rpred 8622 |
. 2
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3 | 1 | rpgt0d 8625 |
. 2
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4 | 2, 3 | jca 290 |
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 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 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rab 2315 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-sn 3381 df-pr 3382 df-op 3384 df-br 3765 df-rp 8584 |
This theorem is referenced by: reclt1d 8636 recgt1d 8637 ltrecd 8641 lerecd 8642 ltrec1d 8643 lerec2d 8644 lediv2ad 8645 ltdiv2d 8646 lediv2d 8647 ledivdivd 8648 divge0d 8663 ltmul1d 8664 ltmul2d 8665 lemul1d 8666 lemul2d 8667 ltdiv1d 8668 lediv1d 8669 ltmuldivd 8670 ltmuldiv2d 8671 lemuldivd 8672 lemuldiv2d 8673 ltdivmuld 8674 ltdivmul2d 8675 ledivmuld 8676 ledivmul2d 8677 ltdiv23d 8683 lediv23d 8684 lt2mul2divd 8685 |
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