Theorem prid2g

Description: An unordered pair contains its second member. Part of Theorem 7.6 of Quine p. 49. (Contributed by Stefan Allan, 8-Nov-2008)

	Ref	Expression
Assertion	prid2g	$$⊢B\in V\to B\in \left\{A,B\right\}$$

Proof

Step	Hyp	Ref	Expression
1		prid1g	$$⊢B\in V\to B\in \left\{B,A\right\}$$
2		prcom	$$⊢\left\{B,A\right\}=\left\{A,B\right\}$$
3	1 2	eleqtrdi	$$⊢B\in V\to B\in \left\{A,B\right\}$$