Description: The ordinal 3 is a natural number. (Contributed by Mario Carneiro, 5-Jan-2016)
Ref | Expression | ||
---|---|---|---|
Assertion | 3onn | ⊢ 3o ∈ ω |
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 |