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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 4169 | . 2 ⊢ ℂ∞ ⊆ (ℂ ∪ ℂ∞) | |
2 | df-bj-ccbar 35899 | . 2 ⊢ ℂ̅ = (ℂ ∪ ℂ∞) | |
3 | 1, 2 | sseqtrri 4015 | 1 ⊢ ℂ∞ ⊆ ℂ̅ |
Colors of variables: wff setvar class |
Syntax hints: ∪ cun 3942 ⊆ wss 3944 ℂcc 11090 ℂ∞cccinfty 35894 ℂ̅cccbar 35898 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-ext 2702 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 846 df-tru 1544 df-ex 1782 df-sb 2068 df-clab 2709 df-cleq 2723 df-clel 2809 df-v 3475 df-un 3949 df-in 3951 df-ss 3961 df-bj-ccbar 35899 |
This theorem is referenced by: bj-pinftyccb 35904 bj-minftyccb 35908 |
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