Theorem sseli

Description: Membership implication from subclass relationship. (Contributed by NM, 5-Aug-1993)

	Ref	Expression
Hypothesis	sseli.1	⊢ 𝐴 ⊆ 𝐵
Assertion	sseli	⊢ ( 𝐶 ∈ 𝐴 → 𝐶 ∈ 𝐵 )

Proof

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