Description: A member of a natural number is a natural number. (Contributed by NM, 21-Jun-1998)
Ref | Expression | ||
---|---|---|---|
Assertion | elnn | ⊢ ( ( 𝐴 ∈ 𝐵 ∧ 𝐵 ∈ ω ) → 𝐴 ∈ ω ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ordom | ⊢ Ord ω | |
2 | ordtr | ⊢ ( Ord ω → Tr ω ) | |
3 | trel | ⊢ ( Tr ω → ( ( 𝐴 ∈ 𝐵 ∧ 𝐵 ∈ ω ) → 𝐴 ∈ ω ) ) | |
4 | 1 2 3 | mp2b | ⊢ ( ( 𝐴 ∈ 𝐵 ∧ 𝐵 ∈ ω ) → 𝐴 ∈ ω ) |