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Theorem bj-ccinftyssccbar 37220
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 4178 . 2 ⊆ (ℂ ∪ ℂ)
2 df-bj-ccbar 37218 . 2 ℂ̅ = (ℂ ∪ ℂ)
31, 2sseqtrri 4032 1 ⊆ ℂ̅
Colors of variables: wff setvar class
Syntax hints:  cun 3948  wss 3950  cc 11154  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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