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Metamath Proof Explorer

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	$⊢ (A \in V \land 0 < \|A\|) \to A \neq \emptyset$

Step	Hyp	Ref	Expression
1		hashneq0	$⊢ A \in V \to (0 < \|A\| \leftrightarrow A \neq \emptyset)$
2	1	biimpa	$⊢ (A \in V \land 0 < \|A\|) \to A \neq \emptyset$