Theorem bj-prfromadj

Description: Unordered pair from adjunction. (Contributed by BJ, 19-Jan-2025) (Proof modification is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		df-pr	$$⊢\left\{x,y\right\}=\left\{x\right\}\cup \left\{y\right\}$$
2		bj-snfromadj	$$⊢\left\{x\right\}\in \mathrm{V}$$
3		bj-adjg1	$$⊢\left\{x\right\}\in \mathrm{V}\to \left\{x\right\}\cup \left\{y\right\}\in \mathrm{V}$$
4	2 3	ax-mp	$$⊢\left\{x\right\}\cup \left\{y\right\}\in \mathrm{V}$$
5	1 4	eqeltri	$$⊢\left\{x,y\right\}\in \mathrm{V}$$