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Mirrors > Home > ILE Home > Th. List > elrpd | Unicode version |
Description: Membership in the set of positive reals. (Contributed by Mario Carneiro, 28-May-2016.) |
Ref | Expression |
---|---|
elrpd.1 |
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elrpd.2 |
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Ref | Expression |
---|---|
elrpd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elrpd.1 |
. 2
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2 | elrpd.2 |
. 2
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3 | elrp 9031 |
. 2
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4 | 1, 2, 3 | sylanbrc 408 |
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 104 ax-ia2 105 ax-ia3 106 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 |
This theorem depends on definitions: df-bi 115 df-3an 922 df-tru 1288 df-nf 1391 df-sb 1688 df-clab 2070 df-cleq 2076 df-clel 2079 df-nfc 2212 df-rab 2362 df-v 2614 df-un 2988 df-sn 3428 df-pr 3429 df-op 3431 df-br 3812 df-rp 9030 |
This theorem is referenced by: zltaddlt1le 9318 modqval 9620 ltexp2a 9844 leexp2a 9845 expnlbnd2 9914 resqrexlem1arp 10265 resqrexlemp1rp 10266 resqrexlemcalc2 10275 resqrexlemcalc3 10276 resqrexlemgt0 10280 resqrexlemglsq 10282 rpsqrtcl 10301 absrpclap 10321 mulcn2 10525 climge0 10537 |
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