Theorem hashgt0n0

Description: If the size of a set is greater than 0, the set is not empty. (Contributed by AV, 5-Aug-2018) (Proof shortened by AV, 18-Nov-2018)

	Ref	Expression
Assertion	hashgt0n0	$$⊢\left(A\in V\wedge 0<\left|A\right|\right)\to A\ne \varnothing$$

Proof

Step	Hyp	Ref	Expression
1		hashneq0	$$⊢A\in V\to \left(0<\left|A\right|\leftrightarrow A\ne \varnothing \right)$$
2	1	biimpa	$$⊢\left(A\in V\wedge 0<\left|A\right|\right)\to A\ne \varnothing$$