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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 9781 |
. 2
| |
| 2 | 1 | rexrd 8121 |
1
|
| Colors of variables: wff set class |
| Syntax hints: |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1469 ax-7 1470 ax-gen 1471 ax-ie1 1515 ax-ie2 1516 ax-8 1526 ax-10 1527 ax-11 1528 ax-i12 1529 ax-bndl 1531 ax-4 1532 ax-17 1548 ax-i9 1552 ax-ial 1556 ax-i5r 1557 ax-ext 2186 |
| This theorem depends on definitions: df-bi 117 df-tru 1375 df-nf 1483 df-sb 1785 df-clab 2191 df-cleq 2197 df-clel 2200 df-nfc 2336 df-rab 2492 df-v 2773 df-un 3169 df-in 3171 df-ss 3178 df-xr 8110 df-rp 9775 |
| This theorem is referenced by: xrminrpcl 11556 blcntrps 14858 blcntr 14859 unirnblps 14865 unirnbl 14866 blssexps 14872 blssex 14873 blin2 14875 neibl 14934 blnei 14935 metss 14937 metss2lem 14940 bdmet 14945 bdmopn 14947 mopnex 14948 metrest 14949 xmettx 14953 metcnp3 14954 metcnp 14955 metcnpi3 14960 txmetcnp 14961 limcimolemlt 15107 |
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