Metamath Proof Explorer

Theorem prmone0

Description: The primorial function is nonzero. (Contributed by AV, 28-Aug-2020)

Ref Expression
Assertion prmone0 
|- ( N e. NN0 -> ( #p ` N ) =/= 0 )

Proof

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