Theorem bj-ccinftyssccbar 37578

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 4108	. 2 ⊢ ℂ∞ ⊆ (ℂ ∪ ℂ∞)
2		df-bj-ccbar 37576	. 2 ⊢ ℂ̅ = (ℂ ∪ ℂ∞)
3	1, 2	sseqtrri 3964	1 ⊢ ℂ∞ ⊆ ℂ̅

Syntax hints:   ∪ cun 3881   ⊆ wss 3883  ℂcc 11027  ℂ_∞cccinfty 37571  ℂ̅cccbar 37575

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2711

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-tru 1550  df-ex 1787  df-sb 2074  df-clab 2718  df-cleq 2731  df-clel 2814  df-v 3433  df-un 3888  df-ss 3900  df-bj-ccbar 37576

This theorem is referenced by:  bj-pinftyccb  37581  bj-minftyccb  37585