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 e. { A } <-> x = A )

Proof

Step Hyp Ref Expression
1 vex 
 |-  x e. _V
2 1 elsn 
 |-  ( x e. { A } <-> x = A )