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Metamath Proof Explorer

Theorem prmone0

Description: The primorial function is nonzero. (Contributed by AV, 28-Aug-2020)

		Ref	Expression
	Assertion	prmone0	$⊢ N \in ℕ_{0} \to #_{p} (N) \neq 0$

Step	Hyp	Ref	Expression
1		prmocl	$⊢ N \in ℕ_{0} \to #_{p} (N) \in ℕ$
2	1	nnne0d	$⊢ N \in ℕ_{0} \to #_{p} (N) \neq 0$