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Metamath Proof Explorer

Theorem elsn2

Description: There is exactly one element in a singleton. Exercise 2 of TakeutiZaring p. 15. This variation requires only that B , rather than A , be a set. (Contributed by NM, 12-Jun-1994)

Ref Expression
Hypothesis elsn2.1 ⊢ B ∈ V
Assertion elsn2 ⊢ A ∈ B ↔ A = B

Proof

Step Hyp Ref Expression
1 elsn2.1 ⊢ B ∈ V
2 elsn2g ⊢ B ∈ V → A ∈ B ↔ A = B
3 1 2 ax-mp ⊢ A ∈ B ↔ A = B