Theorem tpex

Description: An unordered triple of classes exists. (Contributed by NM, 10-Apr-1994)

	Ref	Expression
Assertion	tpex	$$⊢\left\{A,B,C\right\}\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		df-tp	$$⊢\left\{A,B,C\right\}=\left\{A,B\right\}\cup \left\{C\right\}$$
2		prex	$$⊢\left\{A,B\right\}\in \mathrm{V}$$
3		snex	$$⊢\left\{C\right\}\in \mathrm{V}$$
4	2 3	unex	$$⊢\left\{A,B\right\}\cup \left\{C\right\}\in \mathrm{V}$$
5	1 4	eqeltri	$$⊢\left\{A,B,C\right\}\in \mathrm{V}$$