Theorem snsspr2

Description: A singleton is a subset of an unordered pair containing its member. (Contributed by NM, 2-May-2009)

	Ref	Expression
Assertion	snsspr2	$$⊢\left\{B\right\}\subseteq \left\{A,B\right\}$$

Proof

Step	Hyp	Ref	Expression
1		ssun2	$$⊢\left\{B\right\}\subseteq \left\{A\right\}\cup \left\{B\right\}$$
2		df-pr	$$⊢\left\{A,B\right\}=\left\{A\right\}\cup \left\{B\right\}$$
3	1 2	sseqtrri	$$⊢\left\{B\right\}\subseteq \left\{A,B\right\}$$