Theorem atssbase

Description: The set of atoms is a subset of the base set. ( atssch analog.) (Contributed by NM, 21-Oct-2011)

	Ref	Expression
Hypotheses	atombase.b	$$⊢B={\mathrm{Base}}_K$$
	atombase.a	$$⊢A=\mathrm{Atoms}\left(K\right)$$
Assertion	atssbase	$$⊢A\subseteq B$$

Proof

Step	Hyp	Ref	Expression
1		atombase.b	$$⊢B={\mathrm{Base}}_K$$
2		atombase.a	$$⊢A=\mathrm{Atoms}\left(K\right)$$
3	1 2	atbase	$$⊢x\in A\to x\in B$$
4	3	ssriv	$$⊢A\subseteq B$$