Theorem bj-ccinftyssccbar

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

	Ref	Expression
Assertion	bj-ccinftyssccbar	$$⊢{ℂ}_{\infty }\subseteq \overline{ℂ}$$

Proof

Step	Hyp	Ref	Expression
1		ssun2	$$⊢{ℂ}_{\infty }\subseteq ℂ\cup {ℂ}_{\infty }$$
2		df-bj-ccbar	$$⊢\overline{ℂ}=ℂ\cup {ℂ}_{\infty }$$
3	1 2	sseqtrri	$$⊢{ℂ}_{\infty }\subseteq \overline{ℂ}$$