Theorem prnzg

Description: A pair containing a set is not empty. (Contributed by FL, 19-Sep-2011) (Proof shortened by JJ, 23-Jul-2021)

	Ref	Expression
Assertion	prnzg	$$⊢A\in V\to \left\{A,B\right\}\ne \varnothing$$

Proof

Step	Hyp	Ref	Expression
1		prid1g	$$⊢A\in V\to A\in \left\{A,B\right\}$$
2	1	ne0d	$$⊢A\in V\to \left\{A,B\right\}\ne \varnothing$$