Theorem bj-ccssccbar 37160

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 4188	. 2 ⊢ ℂ ⊆ (ℂ ∪ ℂ∞)
2		df-bj-ccbar 37159	. 2 ⊢ ℂ̅ = (ℂ ∪ ℂ∞)
3	1, 2	sseqtrri 4033	1 ⊢ ℂ ⊆ ℂ̅

Syntax hints:   ∪ cun 3961   ⊆ wss 3963  ℂcc 11144  ℂ_∞cccinfty 37154  ℂ̅cccbar 37158

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1963  ax-7 2003  ax-8 2106  ax-9 2114  ax-ext 2704

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-tru 1538  df-ex 1775  df-sb 2061  df-clab 2711  df-cleq 2725  df-clel 2812  df-v 3479  df-un 3968  df-ss 3980  df-bj-ccbar 37159

This theorem is referenced by: (None)