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 = ( Base ‘ 𝐾 )
	atombase.a	⊢ 𝐴 = ( Atoms ‘ 𝐾 )
Assertion	atssbase	⊢ 𝐴 ⊆ 𝐵

Proof

Step	Hyp	Ref	Expression
1		atombase.b	⊢ 𝐵 = ( Base ‘ 𝐾 )
2		atombase.a	⊢ 𝐴 = ( Atoms ‘ 𝐾 )
3	1 2	atbase	⊢ ( 𝑥 ∈ 𝐴 → 𝑥 ∈ 𝐵 )
4	3	ssriv	⊢ 𝐴 ⊆ 𝐵