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Metamath Proof Explorer

Theorem uzxrd

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

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

Proof

Step Hyp Ref Expression
1 uzxrd.1 ⊢ 𝑍 = ( ℤ≥ ‘ 𝑀 )
2 uzxrd.2 ⊢ ( 𝜑 → 𝐴 ∈ 𝑍 )
3 ressxr ⊢ ℝ ⊆ ℝ*
4 1 2 uzred ⊢ ( 𝜑 → 𝐴 ∈ ℝ )
5 3 4 sselid ⊢ ( 𝜑 → 𝐴 ∈ ℝ* )