Theorem bj-snfromadj

Description: Singleton from adjunction and empty set. (Contributed by BJ, 19-Jan-2025) (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-snfromadj	$$⊢\left\{x\right\}\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		0un	$$⊢\varnothing \cup \left\{x\right\}=\left\{x\right\}$$
2		0ex	$$⊢\varnothing \in \mathrm{V}$$
3		bj-adjg1	$$⊢\varnothing \in \mathrm{V}\to \varnothing \cup \left\{x\right\}\in \mathrm{V}$$
4	2 3	ax-mp	$$⊢\varnothing \cup \left\{x\right\}\in \mathrm{V}$$
5	1 4	eqeltrri	$$⊢\left\{x\right\}\in \mathrm{V}$$