Theorem sselii

Description: Membership inference from subclass relationship. (Contributed by NM, 31-May-1999)

	Ref	Expression
Hypotheses	sseli.1	⊢ 𝐴 ⊆ 𝐵
	sselii.2	⊢ 𝐶 ∈ 𝐴
Assertion	sselii	⊢ 𝐶 ∈ 𝐵

Proof

Step	Hyp	Ref	Expression
1		sseli.1	⊢ 𝐴 ⊆ 𝐵
2		sselii.2	⊢ 𝐶 ∈ 𝐴
3	1	sseli	⊢ ( 𝐶 ∈ 𝐴 → 𝐶 ∈ 𝐵 )
4	2 3	ax-mp	⊢ 𝐶 ∈ 𝐵