Theorem bj-ccinftyssccbar 36099

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 4174	. 2 ⊢ ℂ∞ ⊆ (ℂ ∪ ℂ∞)
2		df-bj-ccbar 36097	. 2 ⊢ ℂ̅ = (ℂ ∪ ℂ∞)
3	1, 2	sseqtrri 4020	1 ⊢ ℂ∞ ⊆ ℂ̅

Syntax hints:   ∪ cun 3947   ⊆ wss 3949  ℂcc 11108  ℂ_∞cccinfty 36092  ℂ̅cccbar 36096

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704

This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-un 3954  df-in 3956  df-ss 3966  df-bj-ccbar 36097

This theorem is referenced by:  bj-pinftyccb  36102  bj-minftyccb  36106