Theorem prid1

Description: An unordered pair contains its first member. Part of Theorem 7.6 of Quine p. 49. (Contributed by NM, 24-Jun-1993)

	Ref	Expression
Hypothesis	prid1.1	$$⊢A\in \mathrm{V}$$
Assertion	prid1	$$⊢A\in \left\{A,B\right\}$$

Proof

Step	Hyp	Ref	Expression
1		prid1.1	$$⊢A\in \mathrm{V}$$
2		prid1g	$$⊢A\in \mathrm{V}\to A\in \left\{A,B\right\}$$
3	1 2	ax-mp	$$⊢A\in \left\{A,B\right\}$$