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Mirrors > Home > ILE Home > Th. List > rexrd | Unicode version |
Description: A standard real is an extended real. (Contributed by Mario Carneiro, 28-May-2016.) |
Ref | Expression |
---|---|
rexrd.1 |
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Ref | Expression |
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rexrd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ressxr 7833 |
. 2
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2 | rexrd.1 |
. 2
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3 | 1, 2 | sseldi 3100 |
1
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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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 df-xr 7828 |
This theorem is referenced by: xnn0xr 9069 rpxr 9478 rpxrd 9514 xnegcl 9645 xaddf 9657 xaddval 9658 xnn0lenn0nn0 9678 xposdif 9695 iooshf 9765 icoshftf1o 9804 ioo0 10068 ioom 10069 ico0 10070 ioc0 10071 modqelico 10138 mulqaddmodid 10168 addmodid 10176 elicc4abs 10898 xrmaxiflemcl 11046 xblss2ps 12612 xblss2 12613 blss2ps 12614 blss2 12615 blhalf 12616 cnblcld 12743 ioo2blex 12752 tgioo 12754 cnopnap 12802 suplociccreex 12810 suplociccex 12811 dedekindicc 12819 ivthinclemlm 12820 ivthinclemum 12821 ivthinclemlopn 12822 ivthinclemuopn 12824 ivthdec 12830 sin0pilem2 12911 pilem3 12912 |
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