Metamath Proof Explorer


Theorem eluz3nn

Description: An integer greater than or equal to 3 is a positive integer. (Contributed by Alexander van der Vekens, 17-Sep-2018) (Proof shortened by AV, 30-Nov-2025)

Ref Expression
Assertion eluz3nn
|- ( N e. ( ZZ>= ` 3 ) -> N e. NN )

Proof

Step Hyp Ref Expression
1 uzuzle23
 |-  ( N e. ( ZZ>= ` 3 ) -> N e. ( ZZ>= ` 2 ) )
2 eluz2nn
 |-  ( N e. ( ZZ>= ` 2 ) -> N e. NN )
3 1 2 syl
 |-  ( N e. ( ZZ>= ` 3 ) -> N e. NN )