Definition df-pr

Description: Define unordered pair of classes. Definition 7.1 of Quine p. 48. For example, A e. { 1 , -u 1 } -> ( A ^ 2 ) = 1 ( ex-pr ). They are unordered, so { A , B } = { B , A } as proven by prcom . For a more traditional definition, but requiring a dummy variable, see dfpr2 . { A , A } is also an unordered pair, but also a singleton because of { A } = { A , A } (see dfsn2 ). Therefore, { A , B } is called aproper (unordered) pair iff A =/= B and A and B are sets.

Note: ordered pairs are a completely different object defined below in df-op . When the term "pair" is used without qualifier, it generally means "unordered pair", and the context makes it clear which version is meant. (Contributed by NM, 21-Jun-1993)

	Ref	Expression
Assertion	df-pr	$$⊢\left\{A,B\right\}=\left\{A\right\}\cup \left\{B\right\}$$

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cA	$$classA$$
1		cB	$$classB$$
2	0 1	cpr	$$class\left\{A,B\right\}$$
3	0	csn	$$class\left\{A\right\}$$
4	1	csn	$$class\left\{B\right\}$$
5	3 4	cun	$$class\left(\left\{A\right\}\cup \left\{B\right\}\right)$$
6	2 5	wceq	$$wff\left\{A,B\right\}=\left\{A\right\}\cup \left\{B\right\}$$