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| Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-ccinftyssccbar | Structured version Visualization version GIF version | ||
| Description: Infinite extended complex numbers are extended complex numbers. (Contributed by BJ, 27-Jun-2019.) | 
| Ref | Expression | 
|---|---|
| bj-ccinftyssccbar | ⊢ ℂ∞ ⊆ ℂ̅ | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | ssun2 4178 | . 2 ⊢ ℂ∞ ⊆ (ℂ ∪ ℂ∞) | |
| 2 | df-bj-ccbar 37218 | . 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 11154 ℂ∞cccinfty 37213 ℂ̅cccbar 37217 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1794 ax-4 1808 ax-5 1909 ax-6 1966 ax-7 2006 ax-8 2109 ax-9 2117 ax-ext 2707 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-tru 1542 df-ex 1779 df-sb 2064 df-clab 2714 df-cleq 2728 df-clel 2815 df-v 3481 df-un 3955 df-ss 3967 df-bj-ccbar 37218 | 
| This theorem is referenced by: bj-pinftyccb 37223 bj-minftyccb 37227 | 
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