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Metamath Proof Explorer

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