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Metamath Proof Explorer

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