Theorem tpnz

Description: An unordered triple containing a set is not empty. (Contributed by NM, 10-Apr-1994)

	Ref	Expression
Hypothesis	tpnz.1	$$⊢A\in \mathrm{V}$$
Assertion	tpnz	$$⊢\left\{A,B,C\right\}\ne \varnothing$$

Proof

Step	Hyp	Ref	Expression
1		tpnz.1	$$⊢A\in \mathrm{V}$$
2	1	tpid1	$$⊢A\in \left\{A,B,C\right\}$$
3	2	ne0ii	$$⊢\left\{A,B,C\right\}\ne \varnothing$$