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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 8505 | . 2 ⊢ 7 ∈ ℝ | |
2 | 1 | recni 7500 | 1 ⊢ 7 ∈ ℂ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1438 ℂcc 7348 7c7 8478 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-11 1442 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-resscn 7437 ax-1re 7439 ax-addrcl 7442 |
This theorem depends on definitions: df-bi 115 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-in 3005 df-ss 3012 df-2 8481 df-3 8482 df-4 8483 df-5 8484 df-6 8485 df-7 8486 |
This theorem is referenced by: 7p2e9 8567 7p3e10 8951 7t2e14 8985 7t4e28 8987 7t7e49 8990 cos2bnd 11051 |
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