Theorem bj-ccinftyssccbar 37862

Description: Infinite extended complex numbers are extended complex numbers. (Contributed by BJ, 27-Jun-2019.)

Assertion

Ref	Expression
bj-ccinftyssccbar	⊢ ℂ∞ ⊆ ℂ̅

Proof of Theorem bj-ccinftyssccbar

Step	Hyp	Ref	Expression
1		ssun2 4132	. 2 ⊢ ℂ∞ ⊆ (ℂ ∪ ℂ∞)
2		df-bj-ccbar 37860	. 2 ⊢ ℂ̅ = (ℂ ∪ ℂ∞)
3	1, 2	sseqtrri 3986	1 ⊢ ℂ∞ ⊆ ℂ̅

Syntax hints:   ∪ cun 3903   ⊆ wss 3905  ℂcc 11093  ℂ_∞cccinfty 37855  ℂ̅cccbar 37859

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1573  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-v 3457  df-un 3910  df-ss 3922  df-bj-ccbar 37860

This theorem is referenced by:  bj-pinftyccb  37865  bj-minftyccb  37869