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
|- ( 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 )