Theorem snsspr1

Description: A singleton is a subset of an unordered pair containing its member. (Contributed by NM, 27-Aug-2004)

	Ref	Expression
Assertion	snsspr1	$$⊢\left\{A\right\}\subseteq \left\{A,B\right\}$$

Proof

Step	Hyp	Ref	Expression
1		ssun1	$$⊢\left\{A\right\}\subseteq \left\{A\right\}\cup \left\{B\right\}$$
2		df-pr	$$⊢\left\{A,B\right\}=\left\{A\right\}\cup \left\{B\right\}$$
3	1 2	sseqtrri	$$⊢\left\{A\right\}\subseteq \left\{A,B\right\}$$