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Metamath Proof Explorer

Theorem facne0

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

		Ref	Expression
	Assertion	facne0	$⊢ N \in ℕ_{0} \to N! \neq 0$

Step	Hyp	Ref	Expression
1		faccl	$⊢ N \in ℕ_{0} \to N! \in ℕ$
2	1	nnne0d	$⊢ N \in ℕ_{0} \to N! \neq 0$