Theorem eluzelz2d

Description: A member of an upper set of integers is an integer. (Contributed by Glauco Siliprandi, 23-Oct-2021)

	Ref	Expression
Hypotheses	eluzelz2d.1	⊢ 𝑍 = ( ℤ≥ ‘ 𝑀 )
	eluzelz2d.2	⊢ ( 𝜑 → 𝑁 ∈ 𝑍 )
Assertion	eluzelz2d	⊢ ( 𝜑 → 𝑁 ∈ ℤ )

Proof

Step	Hyp	Ref	Expression
1		eluzelz2d.1	⊢ 𝑍 = ( ℤ≥ ‘ 𝑀 )
2		eluzelz2d.2	⊢ ( 𝜑 → 𝑁 ∈ 𝑍 )
3	1	eluzelz2	⊢ ( 𝑁 ∈ 𝑍 → 𝑁 ∈ ℤ )
4	2 3	syl	⊢ ( 𝜑 → 𝑁 ∈ ℤ )