Metamath Proof Explorer


Theorem 7onn

Description: The ordinal 7 is a natural number. (Contributed by BTernaryTau, 4-Sep-2026)

Ref Expression
Assertion 7onn 7o ∈ ω

Proof

Step Hyp Ref Expression
1 df-7o 7o = suc 6o
2 6onn 6o ∈ ω
3 peano2 ( 6o ∈ ω → suc 6o ∈ ω )
4 2 3 ax-mp suc 6o ∈ ω
5 1 4 eqeltri 7o ∈ ω