Metamath Proof Explorer


Theorem 2onn

Description: The ordinal 2 is a natural number. (Contributed by NM, 28-Sep-2004)

Ref Expression
Assertion 2onn 2o ∈ ω

Proof

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