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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 7835 | . 2 ⊢ (𝐴 ∈ ℝ → 𝐴 ∈ ℝ*) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ 𝐴 ∈ ℝ* |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1481 ℝcr 7643 ℝ*cxr 7823 |
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: cos12dec 11510 halfleoddlt 11627 reeff1oleme 12901 reeff1o 12902 sin0pilem2 12911 neghalfpirx 12923 sincosq1sgn 12955 sincosq2sgn 12956 sincosq4sgn 12958 sinq12gt0 12959 cosq14gt0 12961 cosq23lt0 12962 coseq0q4123 12963 coseq00topi 12964 coseq0negpitopi 12965 cosordlem 12978 cosq34lt1 12979 cos02pilt1 12980 cos0pilt1 12981 ioocosf1o 12983 negpitopissre 12984 iooref1o 13426 taupi 13430 |
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