Metamath Proof Explorer


Theorem 3nn

Description: 3 is a positive integer. (Contributed by NM, 8-Jan-2006)

Ref Expression
Assertion 3nn 3 ∈ ℕ

Proof

Step Hyp Ref Expression
1 df-3 3 = ( 2 + 1 )
2 2nn 2 ∈ ℕ
3 peano2nn ( 2 ∈ ℕ → ( 2 + 1 ) ∈ ℕ )
4 2 3 ax-mp ( 2 + 1 ) ∈ ℕ
5 1 4 eqeltri 3 ∈ ℕ