Metamath Proof Explorer

Theorem vsnex

Description: A singleton built on a setvar is a set. (Contributed by BJ, 15-Jan-2025)

Ref Expression
Assertion vsnex 
|- { x } e. _V

Proof

Step Hyp Ref Expression
1 dfsn2 
 |-  { x } = { x , x }
2 zfpair2 
 |-  { x , x } e. _V
3 1 2 eqeltri 
 |-  { x } e. _V