Theorem snsstp1

Description: A singleton is a subset of an unordered triple containing its member. (Contributed by NM, 9-Oct-2013)

	Ref	Expression
Assertion	snsstp1	$$⊢\left\{A\right\}\subseteq \left\{A,B,C\right\}$$

Proof

Step	Hyp	Ref	Expression
1		snsspr1	$$⊢\left\{A\right\}\subseteq \left\{A,B\right\}$$
2		ssun1	$$⊢\left\{A,B\right\}\subseteq \left\{A,B\right\}\cup \left\{C\right\}$$
3	1 2	sstri	$$⊢\left\{A\right\}\subseteq \left\{A,B\right\}\cup \left\{C\right\}$$
4		df-tp	$$⊢\left\{A,B,C\right\}=\left\{A,B\right\}\cup \left\{C\right\}$$
5	3 4	sseqtrri	$$⊢\left\{A\right\}\subseteq \left\{A,B,C\right\}$$