Metamath Proof Explorer


Theorem 5onn

Description: The ordinal 5 is a natural number. (Contributed by BTernaryTau, 4-Sep-2026)

Ref Expression
Assertion 5onn 5o ∈ ω

Proof

Step Hyp Ref Expression
1 df-5o ⊢ 5o = suc 4o
2 4onn ⊢ 4o ∈ ω
3 peano2 ⊢ ( 4o ∈ ω → suc 4o ∈ ω )
4 2 3 ax-mp ⊢ suc 4o ∈ ω
5 1 4 eqeltri ⊢ 5o ∈ ω