Theorem prprc2

Description: A proper class vanishes in an unordered pair. (Contributed by NM, 22-Mar-2006)

	Ref	Expression
Assertion	prprc2	$$⊢\neg B\in \mathrm{V}\to \left\{A,B\right\}=\left\{A\right\}$$

Proof

Step	Hyp	Ref	Expression
1		prcom	$$⊢\left\{A,B\right\}=\left\{B,A\right\}$$
2		prprc1	$$⊢\neg B\in \mathrm{V}\to \left\{B,A\right\}=\left\{A\right\}$$
3	1 2	eqtrid	$$⊢\neg B\in \mathrm{V}\to \left\{A,B\right\}=\left\{A\right\}$$