Theorem bj-ccinftyssccbar 35901

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 4169	. 2 ⊢ ℂ∞ ⊆ (ℂ ∪ ℂ∞)
2		df-bj-ccbar 35899	. 2 ⊢ ℂ̅ = (ℂ ∪ ℂ∞)
3	1, 2	sseqtrri 4015	1 ⊢ ℂ∞ ⊆ ℂ̅

Syntax hints:   ∪ cun 3942   ⊆ wss 3944  ℂcc 11090  ℂ_∞cccinfty 35894  ℂ̅cccbar 35898

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2702

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2709  df-cleq 2723  df-clel 2809  df-v 3475  df-un 3949  df-in 3951  df-ss 3961  df-bj-ccbar 35899

This theorem is referenced by:  bj-pinftyccb  35904  bj-minftyccb  35908