Theorem bj-ccssccbar 38231

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 4176	. 2 ⊢ ℂ ⊆ (ℂ ∪ ℂ∞)
2		df-bj-ccbar 38230	. 2 ⊢ ℂ̅ = (ℂ ∪ ℂ∞)
3	1, 2	sseqtrri 3957	1 ⊢ ℂ ⊆ ℂ̅

This proof depends on syntax axioms:   ⊆ wss 3895   ∪ cun 4149  ℂcc 11201  ℂ_∞cccinfty 38225  ℂ̅cccbar 38229

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1572  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-v 3452  df-ss 3896  df-un 4151  df-bj-ccbar 38230

This theorem is used by: (None)