Theorem uzred

Description: An upper integer is a real number. (Contributed by Glauco Siliprandi, 2-Jan-2022)

	Ref	Expression
Hypotheses	uzred.1	⊢ 𝑍 = ( ℤ≥ ‘ 𝑀 )
	uzred.2	⊢ ( 𝜑 → 𝐴 ∈ 𝑍 )
Assertion	uzred	⊢ ( 𝜑 → 𝐴 ∈ ℝ )

Proof

Step	Hyp	Ref	Expression
1		uzred.1	⊢ 𝑍 = ( ℤ≥ ‘ 𝑀 )
2		uzred.2	⊢ ( 𝜑 → 𝐴 ∈ 𝑍 )
3		zssre	⊢ ℤ ⊆ ℝ
4	1 2	eluzelz2d	⊢ ( 𝜑 → 𝐴 ∈ ℤ )
5	3 4	sseldi	⊢ ( 𝜑 → 𝐴 ∈ ℝ )