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Mirrors > Home > ILE Home > Th. List > 0xr | Unicode version |
Description: Zero is an extended real. (Contributed by Mario Carneiro, 15-Jun-2014.) |
Ref | Expression |
---|---|
0xr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ressxr 7294 |
. 2
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2 | 0re 7251 |
. 2
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3 | 1, 2 | sselii 3005 |
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 ax-1re 7202 ax-addrcl 7205 ax-rnegex 7217 |
This theorem depends on definitions: df-bi 115 df-tru 1288 df-nf 1391 df-sb 1688 df-clab 2070 df-cleq 2076 df-clel 2079 df-nfc 2212 df-ral 2358 df-rex 2359 df-v 2612 df-un 2986 df-in 2988 df-ss 2995 df-xr 7289 |
This theorem is referenced by: 0lepnf 9011 ge0gtmnf 9036 xlt0neg1 9051 xlt0neg2 9052 xle0neg1 9053 xle0neg2 9054 ioopos 9119 elxrge0 9147 0e0iccpnf 9149 halfleoddlt 10519 |
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