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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 *