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Mirrors > Home > ILE Home > Th. List > 5cn | GIF version |
Description: The number 5 is complex. (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
5cn | ⊢ 5 ∈ ℂ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 5re 8823 | . 2 ⊢ 5 ∈ ℝ | |
2 | 1 | recni 7802 | 1 ⊢ 5 ∈ ℂ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1481 ℂcc 7642 5c5 8798 |
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-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-11 1485 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-resscn 7736 ax-1re 7738 ax-addrcl 7741 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-in 3082 df-ss 3089 df-2 8803 df-3 8804 df-4 8805 df-5 8806 |
This theorem is referenced by: 6m1e5 8867 5p2e7 8890 5p3e8 8891 5p4e9 8892 5p5e10 9276 5t2e10 9305 5recm6rec 9349 ef01bndlem 11499 ex-fac 13111 |
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