![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > rpcnd | GIF version |
Description: A positive real is a complex number. (Contributed by Mario Carneiro, 28-May-2016.) |
Ref | Expression |
---|---|
rpred.1 | ⊢ (φ → A ∈ ℝ+) |
Ref | Expression |
---|---|
rpcnd | ⊢ (φ → A ∈ ℂ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rpred.1 | . . 3 ⊢ (φ → A ∈ ℝ+) | |
2 | 1 | rpred 8397 | . 2 ⊢ (φ → A ∈ ℝ) |
3 | 2 | recnd 6851 | 1 ⊢ (φ → A ∈ ℂ) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∈ wcel 1390 ℂcc 6709 ℝ+crp 8358 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 ax-resscn 6775 |
This theorem depends on definitions: df-bi 110 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-rab 2309 df-in 2918 df-ss 2925 df-rp 8359 |
This theorem is referenced by: rpcnne0d 8406 ltaddrp2d 8427 iccf1o 8642 |
Copyright terms: Public domain | W3C validator |