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| Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-ccssccbar | Structured version Visualization version GIF version | ||
| Description: Complex numbers are extended complex numbers. (Contributed by BJ, 27-Jun-2019.) |
| Ref | Expression |
|---|---|
| bj-ccssccbar | ⊢ ℂ ⊆ ℂ̅ |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ssun1 4177 | . 2 ⊢ ℂ ⊆ (ℂ ∪ ℂ∞) | |
| 2 | df-bj-ccbar 37195 | . 2 ⊢ ℂ̅ = (ℂ ∪ ℂ∞) | |
| 3 | 1, 2 | sseqtrri 4032 | 1 ⊢ ℂ ⊆ ℂ̅ |
| Colors of variables: wff setvar class |
| Syntax hints: ∪ cun 3948 ⊆ wss 3950 ℂcc 11149 ℂ∞cccinfty 37190 ℂ̅cccbar 37194 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2707 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-tru 1543 df-ex 1780 df-sb 2065 df-clab 2714 df-cleq 2728 df-clel 2815 df-v 3481 df-un 3955 df-ss 3967 df-bj-ccbar 37195 |
| This theorem is referenced by: (None) |
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