Theorem ssel2

Description: Membership relationships follow from a subclass relationship. (Contributed by NM, 7-Jun-2004)

	Ref	Expression
Assertion	ssel2	⊢ ( ( 𝐴 ⊆ 𝐵 ∧ 𝐶 ∈ 𝐴 ) → 𝐶 ∈ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		ssel	⊢ ( 𝐴 ⊆ 𝐵 → ( 𝐶 ∈ 𝐴 → 𝐶 ∈ 𝐵 ) )
2	1	imp	⊢ ( ( 𝐴 ⊆ 𝐵 ∧ 𝐶 ∈ 𝐴 ) → 𝐶 ∈ 𝐵 )