Theorem elfzelzd

Description: A member of a finite set of sequential integers is an integer. (Contributed by Glauco Siliprandi, 5-Apr-2020)

	Ref	Expression
Hypothesis	elfzelzd.1	⊢ ( 𝜑 → 𝐾 ∈ ( 𝑀 ... 𝑁 ) )
Assertion	elfzelzd	⊢ ( 𝜑 → 𝐾 ∈ ℤ )

Proof

Step	Hyp	Ref	Expression
1		elfzelzd.1	⊢ ( 𝜑 → 𝐾 ∈ ( 𝑀 ... 𝑁 ) )
2		elfzelz	⊢ ( 𝐾 ∈ ( 𝑀 ... 𝑁 ) → 𝐾 ∈ ℤ )
3	1 2	syl	⊢ ( 𝜑 → 𝐾 ∈ ℤ )