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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 4148 | . 2 ⊢ ℂ ⊆ (ℂ ∪ ℂ∞) | |
2 | df-bj-ccbar 34501 | . 2 ⊢ ℂ̅ = (ℂ ∪ ℂ∞) | |
3 | 1, 2 | sseqtrri 4004 | 1 ⊢ ℂ ⊆ ℂ̅ |
Colors of variables: wff setvar class |
Syntax hints: ∪ cun 3934 ⊆ wss 3936 ℂcc 10535 ℂ∞cccinfty 34496 ℂ̅cccbar 34500 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-v 3496 df-un 3941 df-in 3943 df-ss 3952 df-bj-ccbar 34501 |
This theorem is referenced by: (None) |
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