Description: Membership in a finite set of sequential integers containing one integer. (Contributed by NM, 21-Jul-2005)
Ref | Expression | ||
---|---|---|---|
Assertion | elfz3 | ⊢ ( 𝑁 ∈ ℤ → 𝑁 ∈ ( 𝑁 ... 𝑁 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uzid | ⊢ ( 𝑁 ∈ ℤ → 𝑁 ∈ ( ℤ≥ ‘ 𝑁 ) ) | |
2 | eluzfz1 | ⊢ ( 𝑁 ∈ ( ℤ≥ ‘ 𝑁 ) → 𝑁 ∈ ( 𝑁 ... 𝑁 ) ) | |
3 | 1 2 | syl | ⊢ ( 𝑁 ∈ ℤ → 𝑁 ∈ ( 𝑁 ... 𝑁 ) ) |