Theorem prmone0

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

	Ref	Expression
Assertion	prmone0	$$⊢N\in {\mathbb{N}}_0\to {\#}_p\left(N\right)\ne 0$$

Proof

Step	Hyp	Ref	Expression
1		prmocl	$$⊢N\in {\mathbb{N}}_0\to {\#}_p\left(N\right)\in \mathbb{N}$$
2	1	nnne0d	$$⊢N\in {\mathbb{N}}_0\to {\#}_p\left(N\right)\ne 0$$