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Mirrors > Home > ILE Home > Th. List > 9cn | GIF version |
Description: The number 9 is complex. (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
9cn | ⊢ 9 ∈ ℂ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 9re 8563 | . 2 ⊢ 9 ∈ ℝ | |
2 | 1 | recni 7554 | 1 ⊢ 9 ∈ ℂ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1439 ℂcc 7402 9c9 8534 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-11 1443 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-resscn 7491 ax-1re 7493 ax-addrcl 7496 |
This theorem depends on definitions: df-bi 116 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-in 3006 df-ss 3013 df-2 8535 df-3 8536 df-4 8537 df-5 8538 df-6 8539 df-7 8540 df-8 8541 df-9 8542 |
This theorem is referenced by: 10m1e9 9026 9t2e18 9052 9t8e72 9058 9t9e81 9059 9t11e99 9060 0.999... 10969 cos2bnd 11105 3dvdsdec 11197 3dvds2dec 11198 |
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