Theorem facne0

Description: The factorial function is nonzero. (Contributed by NM, 26-Apr-2005)

	Ref	Expression
Assertion	facne0	⊢ ( 𝑁 ∈ ℕ0 → ( ! ‘ 𝑁 ) ≠ 0 )

Proof

Step	Hyp	Ref	Expression
1		faccl	⊢ ( 𝑁 ∈ ℕ0 → ( ! ‘ 𝑁 ) ∈ ℕ )
2	1	nnne0d	⊢ ( 𝑁 ∈ ℕ0 → ( ! ‘ 𝑁 ) ≠ 0 )