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 } ∈ V

Proof

Step Hyp Ref Expression
1 dfsn2 { 𝑥 } = { 𝑥 , 𝑥 }
2 zfpair2 { 𝑥 , 𝑥 } ∈ V
3 1 2 eqeltri { 𝑥 } ∈ V