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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

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