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Mirrors > Home > ILE Home > Th. List > rexr | GIF version |
Description: A standard real is an extended real. (Contributed by NM, 14-Oct-2005.) |
Ref | Expression |
---|---|
rexr | ⊢ (𝐴 ∈ ℝ → 𝐴 ∈ ℝ*) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ressxr 7950 | . 2 ⊢ ℝ ⊆ ℝ* | |
2 | 1 | sseli 3143 | 1 ⊢ (𝐴 ∈ ℝ → 𝐴 ∈ ℝ*) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∈ wcel 2141 ℝcr 7760 ℝ*cxr 7940 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-xr 7945 |
This theorem is referenced by: rexri 7964 lenlt 7982 ltpnf 9724 mnflt 9727 xrltnsym 9737 xrlttr 9739 xrltso 9740 xrre 9764 xrre3 9766 xltnegi 9779 rexadd 9796 xaddnemnf 9801 xaddnepnf 9802 xaddcom 9805 xnegdi 9812 xpncan 9815 xnpcan 9816 xleadd1a 9817 xleadd1 9819 xltadd1 9820 xltadd2 9821 xsubge0 9825 xposdif 9826 elioo4g 9878 elioc2 9880 elico2 9881 elicc2 9882 iccss 9885 iooshf 9896 iooneg 9932 icoshft 9934 qbtwnxr 10201 modqmuladdim 10310 elicc4abs 11045 icodiamlt 11131 xrmaxrecl 11205 xrmaxaddlem 11210 xrminrecl 11223 bl2in 13156 blssps 13180 blss 13181 reopnap 13291 bl2ioo 13295 blssioo 13298 sincosq2sgn 13501 sincosq3sgn 13502 sincos6thpi 13516 |
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