Theorem bj-ccssccbar 36588

Description: Complex numbers are extended complex numbers. (Contributed by BJ, 27-Jun-2019.)

Assertion

Ref	Expression
bj-ccssccbar	⊢ ℂ ⊆ ℂ̅

Proof of Theorem bj-ccssccbar

Step	Hyp	Ref	Expression
1		ssun1 4164	. 2 ⊢ ℂ ⊆ (ℂ ∪ ℂ∞)
2		df-bj-ccbar 36587	. 2 ⊢ ℂ̅ = (ℂ ∪ ℂ∞)
3	1, 2	sseqtrri 4011	1 ⊢ ℂ ⊆ ℂ̅

Syntax hints:   ∪ cun 3938   ⊆ wss 3940  ℂcc 11104  ℂ_∞cccinfty 36582  ℂ̅cccbar 36586

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-v 3468  df-un 3945  df-in 3947  df-ss 3957  df-bj-ccbar 36587

This theorem is referenced by: (None)