Theorem shsub2i

Description: Subspace sum is an upper bound of its arguments. (Contributed by NM, 17-Dec-2004) (New usage is discouraged.)

	Ref	Expression
Hypotheses	shincl.1	$$⊢A\in {\mathbf{S}}_{\mathscr{H}}$$
	shincl.2	$$⊢B\in {\mathbf{S}}_{\mathscr{H}}$$
Assertion	shsub2i	$$⊢A\subseteq B{+}_{\mathscr{H}}A$$

Proof

Step	Hyp	Ref	Expression
1		shincl.1	$$⊢A\in {\mathbf{S}}_{\mathscr{H}}$$
2		shincl.2	$$⊢B\in {\mathbf{S}}_{\mathscr{H}}$$
3	2 1	shsel2i	$$⊢x\in A\to x\in \left(B{+}_{\mathscr{H}}A\right)$$
4	3	ssriv	$$⊢A\subseteq B{+}_{\mathscr{H}}A$$