Theorem facne0

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

	Ref	Expression
Assertion	facne0	$$⊢N\in {\mathbb{N}}_0\to N!\ne 0$$

Proof

Step	Hyp	Ref	Expression
1		faccl	$$⊢N\in {\mathbb{N}}_0\to N!\in \mathbb{N}$$
2	1	nnne0d	$$⊢N\in {\mathbb{N}}_0\to N!\ne 0$$