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Metamath Proof Explorer

Theorem velsn

Description: There is only one element in a singleton. Exercise 2 of TakeutiZaring p. 15. (Contributed by NM, 21-Jun-1993)

Ref Expression
Assertion velsn ( 𝑥 ∈ { 𝐴 } ↔ 𝑥 = 𝐴 )

Proof

Step Hyp Ref Expression
1 vex ⊢ 𝑥 ∈ V
2 1 elsn ⊢ ( 𝑥 ∈ { 𝐴 } ↔ 𝑥 = 𝐴 )