Metamath Proof Explorer

Theorem facne0

Description: The factorial function is nonzero. (Contributed by NM, 26-Apr-2005)

Ref Expression
Assertion facne0 
|- ( N e. NN0 -> ( ! ` N ) =/= 0 )

Proof

Step Hyp Ref Expression
1 faccl 
 |-  ( N e. NN0 -> ( ! ` N ) e. NN )
2 1 nnne0d 
 |-  ( N e. NN0 -> ( ! ` N ) =/= 0 )