Theorem fzossz

Description: A half-open integer interval is a set of integers. (Contributed by Glauco Siliprandi, 8-Apr-2021)

	Ref	Expression
Assertion	fzossz	⊢ ( 𝑀 ..^ 𝑁 ) ⊆ ℤ

Proof

Step	Hyp	Ref	Expression
1		fzossfz	⊢ ( 𝑀 ..^ 𝑁 ) ⊆ ( 𝑀 ... 𝑁 )
2		fzssz	⊢ ( 𝑀 ... 𝑁 ) ⊆ ℤ
3	1 2	sstri	⊢ ( 𝑀 ..^ 𝑁 ) ⊆ ℤ