Theorem prmone0

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

	Ref	Expression
Assertion	prmone0	⊢ ( 𝑁 ∈ ℕ0 → ( #p ‘ 𝑁 ) ≠ 0 )

Proof

Step	Hyp	Ref	Expression
1		prmocl	⊢ ( 𝑁 ∈ ℕ0 → ( #p ‘ 𝑁 ) ∈ ℕ )
2	1	nnne0d	⊢ ( 𝑁 ∈ ℕ0 → ( #p ‘ 𝑁 ) ≠ 0 )