Theorem bj-rvecsscvec

Description: Real vector spaces are subcomplex vector spaces. (Contributed by BJ, 6-Jan-2024)

	Ref	Expression
Assertion	bj-rvecsscvec	$$⊢\mathrm{ℝVec}\subseteq \mathrm{ℂVec}$$

Proof

Step	Hyp	Ref	Expression
1		bj-rvecsscmod	$$⊢\mathrm{ℝVec}\subseteq \mathrm{CMod}$$
2		bj-rvecssvec	$$⊢\mathrm{ℝVec}\subseteq \mathrm{LVec}$$
3	1 2	ssini	$$⊢\mathrm{ℝVec}\subseteq \mathrm{CMod}\cap \mathrm{LVec}$$
4		df-cvs	$$⊢\mathrm{ℂVec}=\mathrm{CMod}\cap \mathrm{LVec}$$
5	3 4	sseqtrri	$$⊢\mathrm{ℝVec}\subseteq \mathrm{ℂVec}$$