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Metamath Proof Explorer

Theorem sselid

Description: Membership inference from subclass relationship. (Contributed by NM, 25-Jun-2014)

Ref Expression
Hypotheses sseli.1 ⊢ A ⊆ B
sselid.2 ⊢ φ → C ∈ A
Assertion sselid ⊢ φ → C ∈ B

Proof

Step Hyp Ref Expression
1 sseli.1 ⊢ A ⊆ B
2 sselid.2 ⊢ φ → C ∈ A
3 1 sseli ⊢ C ∈ A → C ∈ B
4 2 3 syl ⊢ φ → C ∈ B