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Metamath Proof Explorer

Theorem faccld

Description: Closure of the factorial function, deduction version of faccl . (Contributed by Glauco Siliprandi, 5-Apr-2020)

		Ref	Expression
	Hypothesis	faccld.1	$⊢ φ \to N \in ℕ_{0}$
	Assertion	faccld	$⊢ φ \to N! \in ℕ$

Step	Hyp	Ref	Expression
1		faccld.1	$⊢ φ \to N \in ℕ_{0}$
2		faccl	$⊢ N \in ℕ_{0} \to N! \in ℕ$
3	1 2	syl	$⊢ φ \to N! \in ℕ$