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 N 0
Assertion faccld φ N !

Proof

Step Hyp Ref Expression
1 faccld.1 φ N 0
2 faccl N 0 N !
3 1 2 syl φ N !