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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 8807 | . 2 ⊢ 9 ∈ ℝ | |
2 | 1 | recni 7778 | 1 ⊢ 9 ∈ ℂ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1480 ℂcc 7618 9c9 8778 |
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 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-resscn 7712 ax-1re 7714 ax-addrcl 7717 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-in 3077 df-ss 3084 df-2 8779 df-3 8780 df-4 8781 df-5 8782 df-6 8783 df-7 8784 df-8 8785 df-9 8786 |
This theorem is referenced by: 10m1e9 9277 9t2e18 9303 9t8e72 9309 9t9e81 9310 9t11e99 9311 0.999... 11290 cos2bnd 11467 3dvdsdec 11562 3dvds2dec 11563 |
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