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Metamath Proof Explorer

Theorem elsni

Description: There is at most one element in a singleton. (Contributed by NM, 5-Jun-1994)

Ref Expression
Assertion elsni ⊢ A ∈ B → A = B

Proof

Step Hyp Ref Expression
1 elsng ⊢ A ∈ B → A ∈ B ↔ A = B
2 1 ibi ⊢ A ∈ B → A = B