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Theorem bj-ccssccbar 33433
 Description: Complex numbers are extended complex numbers. (Contributed by BJ, 27-Jun-2019.)
Assertion
Ref Expression
bj-ccssccbar ℂ ⊆ ℂ̅

Proof of Theorem bj-ccssccbar
StepHypRef Expression
1 ssun1 3919 . 2 ℂ ⊆ (ℂ ∪ ℂ)
2 df-bj-ccbar 33432 . 2 ℂ̅ = (ℂ ∪ ℂ)
31, 2sseqtr4i 3779 1 ℂ ⊆ ℂ̅
 Colors of variables: wff setvar class Syntax hints:   ∪ cun 3713   ⊆ wss 3715  ℂcc 10146  ℂ∞cccinfty 33427  ℂ̅cccbar 33431 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-nfc 2891  df-v 3342  df-un 3720  df-in 3722  df-ss 3729  df-bj-ccbar 33432 This theorem is referenced by: (None)
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