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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 8767 | . 2 ⊢ 5 ∈ ℝ | |
2 | 1 | recni 7746 | 1 ⊢ 5 ∈ ℂ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1465 ℂcc 7586 5c5 8742 |
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 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-11 1469 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-resscn 7680 ax-1re 7682 ax-addrcl 7685 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-in 3047 df-ss 3054 df-2 8747 df-3 8748 df-4 8749 df-5 8750 |
This theorem is referenced by: 6m1e5 8811 5p2e7 8834 5p3e8 8835 5p4e9 8836 5p5e10 9220 5t2e10 9249 5recm6rec 9293 ef01bndlem 11390 ex-fac 12867 |
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