Theorem faccld

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

	Ref	Expression
Hypothesis	faccld.1	|- ( ph -> N e. NN0 )
Assertion	faccld	|- ( ph -> ( ! ` N ) e. NN )

Proof

Step	Hyp	Ref	Expression
1		faccld.1	|- ( ph -> N e. NN0 )
2		faccl	|- ( N e. NN0 -> ( ! ` N ) e. NN )
3	1 2	syl	|- ( ph -> ( ! ` N ) e. NN )