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Metamath Proof Explorer

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