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Mirrors > Home > ILE Home > Th. List > rpxr | GIF version |
Description: A positive real is an extended real. (Contributed by Mario Carneiro, 21-Aug-2015.) |
Ref | Expression |
---|---|
rpxr | ⊢ (𝐴 ∈ ℝ+ → 𝐴 ∈ ℝ*) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rpre 9049 | . 2 ⊢ (𝐴 ∈ ℝ+ → 𝐴 ∈ ℝ) | |
2 | 1 | rexrd 7458 | 1 ⊢ (𝐴 ∈ ℝ+ → 𝐴 ∈ ℝ*) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∈ wcel 1436 ℝ*cxr 7442 ℝ+crp 9043 |
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 1379 ax-7 1380 ax-gen 1381 ax-ie1 1425 ax-ie2 1426 ax-8 1438 ax-10 1439 ax-11 1440 ax-i12 1441 ax-bndl 1442 ax-4 1443 ax-17 1462 ax-i9 1466 ax-ial 1470 ax-i5r 1471 ax-ext 2067 |
This theorem depends on definitions: df-bi 115 df-tru 1290 df-nf 1393 df-sb 1690 df-clab 2072 df-cleq 2078 df-clel 2081 df-nfc 2214 df-rab 2364 df-v 2616 df-un 2990 df-in 2992 df-ss 2999 df-xr 7447 df-rp 9044 |
This theorem is referenced by: (None) |
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