Theorem bj-ccinftyssccbar 37201

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 4189	. 2 ⊢ ℂ∞ ⊆ (ℂ ∪ ℂ∞)
2		df-bj-ccbar 37199	. 2 ⊢ ℂ̅ = (ℂ ∪ ℂ∞)
3	1, 2	sseqtrri 4033	1 ⊢ ℂ∞ ⊆ ℂ̅

Syntax hints:   ∪ cun 3961   ⊆ wss 3963  ℂcc 11151  ℂ_∞cccinfty 37194  ℂ̅cccbar 37198

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-un 3968  df-ss 3980  df-bj-ccbar 37199

This theorem is referenced by:  bj-pinftyccb  37204  bj-minftyccb  37208