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Mirrors > Home > ILE Home > Th. List > rexri | GIF version |
Description: A standard real is an extended real (inference form.) (Contributed by David Moews, 28-Feb-2017.) |
Ref | Expression |
---|---|
rexri.1 | ⊢ 𝐴 ∈ ℝ |
Ref | Expression |
---|---|
rexri | ⊢ 𝐴 ∈ ℝ* |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rexri.1 | . 2 ⊢ 𝐴 ∈ ℝ | |
2 | rexr 7980 | . 2 ⊢ (𝐴 ∈ ℝ → 𝐴 ∈ ℝ*) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ 𝐴 ∈ ℝ* |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2148 ℝcr 7788 ℝ*cxr 7968 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-xr 7973 |
This theorem is referenced by: 1xr 7993 cos12dec 11746 halfleoddlt 11869 reeff1oleme 13826 reeff1o 13827 sin0pilem2 13836 neghalfpirx 13848 sincosq1sgn 13880 sincosq2sgn 13881 sincosq4sgn 13883 sinq12gt0 13884 cosq14gt0 13886 cosq23lt0 13887 coseq0q4123 13888 coseq00topi 13889 coseq0negpitopi 13890 cosordlem 13903 cosq34lt1 13904 cos02pilt1 13905 cos0pilt1 13906 ioocosf1o 13908 negpitopissre 13909 iooref1o 14405 taupi 14441 |
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