Theorem bj-ccssccbar 37584

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 4114	. 2 ⊢ ℂ ⊆ (ℂ ∪ ℂ∞)
2		df-bj-ccbar 37583	. 2 ⊢ ℂ̅ = (ℂ ∪ ℂ∞)
3	1, 2	sseqtrri 3971	1 ⊢ ℂ ⊆ ℂ̅

Syntax hints:   ∪ cun 3888   ⊆ wss 3890  ℂcc 11034  ℂ_∞cccinfty 37578  ℂ̅cccbar 37582

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 2712

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 2719  df-cleq 2732  df-clel 2815  df-v 3434  df-un 3895  df-ss 3907  df-bj-ccbar 37583

This theorem is referenced by: (None)