Theorem eluzfz2b

Description: Membership in a finite set of sequential integers - special case. (Contributed by NM, 14-Sep-2005)

	Ref	Expression
Assertion	eluzfz2b	⊢ ( 𝑁 ∈ ( ℤ≥ ‘ 𝑀 ) ↔ 𝑁 ∈ ( 𝑀 ... 𝑁 ) )

Proof

Step	Hyp	Ref	Expression
1		eluzfz2	⊢ ( 𝑁 ∈ ( ℤ≥ ‘ 𝑀 ) → 𝑁 ∈ ( 𝑀 ... 𝑁 ) )
2		elfzuz	⊢ ( 𝑁 ∈ ( 𝑀 ... 𝑁 ) → 𝑁 ∈ ( ℤ≥ ‘ 𝑀 ) )
3	1 2	impbii	⊢ ( 𝑁 ∈ ( ℤ≥ ‘ 𝑀 ) ↔ 𝑁 ∈ ( 𝑀 ... 𝑁 ) )