Theorem bj-ccssccbar 33433

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 3919	. 2 ⊢ ℂ ⊆ (ℂ ∪ ℂ∞)
2		df-bj-ccbar 33432	. 2 ⊢ ℂ̅ = (ℂ ∪ ℂ∞)
3	1, 2	sseqtr4i 3779	1 ⊢ ℂ ⊆ ℂ̅

Syntax hints:   ∪ cun 3713   ⊆ wss 3715  ℂcc 10146  ℂ_∞cccinfty 33427  ℂ̅cccbar 33431

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740

This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-nfc 2891  df-v 3342  df-un 3720  df-in 3722  df-ss 3729  df-bj-ccbar 33432

This theorem is referenced by: (None)