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Mirrors > Home > ILE Home > Th. List > rpxr | Unicode version |
Description: A positive real is an extended real. (Contributed by Mario Carneiro, 21-Aug-2015.) |
Ref | Expression |
---|---|
rpxr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rpre 9416 | . 2 | |
2 | 1 | rexrd 7783 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1465 cxr 7767 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-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-xr 7772 df-rp 9410 |
This theorem is referenced by: xrminrpcl 11011 blcntrps 12511 blcntr 12512 unirnblps 12518 unirnbl 12519 blssexps 12525 blssex 12526 blin2 12528 neibl 12587 blnei 12588 metss 12590 metss2lem 12593 bdmet 12598 bdmopn 12600 mopnex 12601 metrest 12602 xmettx 12606 metcnp3 12607 metcnp 12608 metcnpi3 12613 txmetcnp 12614 limcimolemlt 12729 |
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