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Mirrors > Home > ILE Home > Th. List > rpcn | GIF version |
Description: A positive real is a complex number. (Contributed by NM, 11-Nov-2008.) |
Ref | Expression |
---|---|
rpcn | ⊢ (𝐴 ∈ ℝ+ → 𝐴 ∈ ℂ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rpre 8740 | . 2 ⊢ (𝐴 ∈ ℝ+ → 𝐴 ∈ ℝ) | |
2 | 1 | recnd 7147 | 1 ⊢ (𝐴 ∈ ℝ+ → 𝐴 ∈ ℂ) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∈ wcel 1433 ℂcc 6979 ℝ+crp 8734 |
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 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-resscn 7068 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-rab 2357 df-in 2979 df-ss 2986 df-rp 8735 |
This theorem is referenced by: rpcnne0 8753 rpcnap0 8754 divge1 8800 sqrtdiv 9928 |
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