Theorem faccld

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

	Ref	Expression
Hypothesis	faccld.1	$$⊢\phi \to N\in {\mathbb{N}}_0$$
Assertion	faccld	$$⊢\phi \to N!\in \mathbb{N}$$

Proof

Step	Hyp	Ref	Expression
1		faccld.1	$$⊢\phi \to N\in {\mathbb{N}}_0$$
2		faccl	$$⊢N\in {\mathbb{N}}_0\to N!\in \mathbb{N}$$
3	1 2	syl	$$⊢\phi \to N!\in \mathbb{N}$$