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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ressxr 7802 | . 2 | |
2 | 0re 7759 | . 2 | |
3 | 1, 2 | sselii 3089 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1480 cr 7612 cc0 7613 cxr 7792 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-1re 7707 ax-addrcl 7710 ax-rnegex 7722 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-xr 7797 |
This theorem is referenced by: 0lepnf 9569 ge0gtmnf 9599 xlt0neg1 9614 xlt0neg2 9615 xle0neg1 9616 xle0neg2 9617 xaddf 9620 xaddval 9621 xaddid1 9638 xaddid2 9639 xnn0xadd0 9643 xaddge0 9654 xsubge0 9657 xposdif 9658 ioopos 9726 elxrge0 9754 0e0iccpnf 9756 xrmaxadd 11023 xrminrpcl 11036 xrbdtri 11038 ef01bndlem 11452 sin01bnd 11453 cos01bnd 11454 cos1bnd 11455 sin01gt0 11457 cos01gt0 11458 sin02gt0 11459 sincos1sgn 11460 sincos2sgn 11461 cos12dec 11463 halfleoddlt 11580 psmetge0 12489 isxmet2d 12506 xmetge0 12523 blgt0 12560 xblss2ps 12562 xblss2 12563 xblm 12575 bdxmet 12659 bdmet 12660 bdmopn 12662 xmetxp 12665 cnblcld 12693 blssioo 12703 sin0pilem1 12851 sin0pilem2 12852 pilem3 12853 sinhalfpilem 12861 sincosq1lem 12895 sincosq1sgn 12896 sincosq2sgn 12897 sinq12gt0 12900 cosq14gt0 12902 tangtx 12908 sincos4thpi 12910 pigt3 12914 cosordlem 12919 cosq34lt1 12920 cos02pilt1 12921 taupi 13228 |
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