This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

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 sselid ⊢ ( 𝜑 → 𝐴 ∈ ℝ )