Theorem bj-ccinftyssccbar 37157

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 4152	. 2 ⊢ ℂ∞ ⊆ (ℂ ∪ ℂ∞)
2		df-bj-ccbar 37155	. 2 ⊢ ℂ̅ = (ℂ ∪ ℂ∞)
3	1, 2	sseqtrri 4006	1 ⊢ ℂ∞ ⊆ ℂ̅

Syntax hints:   ∪ cun 3922   ⊆ wss 3924  ℂcc 11119  ℂ_∞cccinfty 37150  ℂ̅cccbar 37154

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2713  df-cleq 2726  df-clel 2808  df-v 3459  df-un 3929  df-ss 3941  df-bj-ccbar 37155

This theorem is referenced by:  bj-pinftyccb  37160  bj-minftyccb  37164