Metamath Proof Explorer


Theorem 3onn

Description: The ordinal 3 is a natural number. (Contributed by Mario Carneiro, 5-Jan-2016)

Ref Expression
Assertion 3onn 3o ∈ ω

Proof

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