Theorem eluzelzd

Description: A member of an upper set of integers is an integer. (Contributed by Glauco Siliprandi, 8-Apr-2021)

	Ref	Expression
Hypothesis	eluzelzd.1	⊢ ( 𝜑 → 𝑁 ∈ ( ℤ≥ ‘ 𝑀 ) )
Assertion	eluzelzd	⊢ ( 𝜑 → 𝑁 ∈ ℤ )

Proof

Step	Hyp	Ref	Expression
1		eluzelzd.1	⊢ ( 𝜑 → 𝑁 ∈ ( ℤ≥ ‘ 𝑀 ) )
2		eluzelz	⊢ ( 𝑁 ∈ ( ℤ≥ ‘ 𝑀 ) → 𝑁 ∈ ℤ )
3	1 2	syl	⊢ ( 𝜑 → 𝑁 ∈ ℤ )