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Metamath Proof Explorer

Theorem snidb

Description: A class is a set iff it is a member of its singleton. (Contributed by NM, 5-Apr-2004)

Ref Expression
Assertion snidb ⊢ A ∈ V ↔ A ∈ A

Proof

Step Hyp Ref Expression
1 snidg ⊢ A ∈ V → A ∈ A
2 elex ⊢ A ∈ A → A ∈ V
3 1 2 impbii ⊢ A ∈ V ↔ A ∈ A