Theorem prid2

Description: An unordered pair contains its second member. Part of Theorem 7.6 of Quine p. 49. (Note: the proof from prid2g and ax-mp has one fewer essential step but one more total step.) (Contributed by NM, 5-Aug-1993)

	Ref	Expression
Hypothesis	prid2.1	|- B e. _V
Assertion	prid2	|- B e. { A , B }

Proof

Step	Hyp	Ref	Expression
1		prid2.1	|- B e. _V
2	1	prid1	|- B e. { B , A }
3		prcom	|- { B , A } = { A , B }
4	2 3	eleqtri	|- B e. { A , B }