Metamath Proof Explorer


Theorem 4nn

Description: 4 is a positive integer. (Contributed by NM, 8-Jan-2006)

Ref Expression
Assertion 4nn 4 ∈ ℕ

Proof

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