Description: The ordinal 7 is a natural number. (Contributed by BTernaryTau, 4-Sep-2026)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | 7onn | ⊢ 7o ∈ ω |
| 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 |