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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 8771 | . 2 ⊢ 7 ∈ ℝ | |
2 | 1 | recni 7746 | 1 ⊢ 7 ∈ ℂ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1465 ℂcc 7586 7c7 8744 |
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 df-6 8751 df-7 8752 |
This theorem is referenced by: 8m1e7 8813 7p2e9 8839 7p3e10 9224 7t2e14 9258 7t4e28 9260 7t7e49 9263 cos2bnd 11394 |
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