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Theorem bj-ccinftyssccbar 32282
 Description: Infinite extended complex numbers are extended complex numbers. (Contributed by BJ, 27-Jun-2019.)
Assertion
Ref Expression
bj-ccinftyssccbar ⊆ ℂ̅

Proof of Theorem bj-ccinftyssccbar
StepHypRef Expression
1 ssun2 3739 . 2 ⊆ (ℂ ∪ ℂ)
2 df-bj-ccbar 32280 . 2 ℂ̅ = (ℂ ∪ ℂ)
31, 2sseqtr4i 3601 1 ⊆ ℂ̅
 Colors of variables: wff setvar class Syntax hints:   ∪ cun 3538   ⊆ wss 3540  ℂcc 9813  ℂ∞cccinfty 32275  ℂ̅cccbar 32279 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-un 3545  df-in 3547  df-ss 3554  df-bj-ccbar 32280 This theorem is referenced by:  bj-pinftyccb  32285  bj-minftyccb  32289
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