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Mirrors > Home > ILE Home > Th. List > 7cn | GIF version |
Description: The number 7 is complex. (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
7cn | ⊢ 7 ∈ ℂ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 7re 8932 | . 2 ⊢ 7 ∈ ℝ | |
2 | 1 | recni 7903 | 1 ⊢ 7 ∈ ℂ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2135 ℂcc 7743 7c7 8905 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-11 1493 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 ax-resscn 7837 ax-1re 7839 ax-addrcl 7842 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-in 3118 df-ss 3125 df-2 8908 df-3 8909 df-4 8910 df-5 8911 df-6 8912 df-7 8913 |
This theorem is referenced by: 8m1e7 8974 7p2e9 9000 7p3e10 9388 7t2e14 9422 7t4e28 9424 7t7e49 9427 cos2bnd 11691 |
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