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Theorem zxrd 43695
Description: An integer is an extended real number. (Contributed by Glauco Siliprandi, 2-Jan-2022.)
Hypothesis
Ref Expression
zxrd.1 (𝜑𝐴 ∈ ℤ)
Assertion
Ref Expression
zxrd (𝜑𝐴 ∈ ℝ*)

Proof of Theorem zxrd
StepHypRef Expression
1 zxrd.1 . . 3 (𝜑𝐴 ∈ ℤ)
21zred 12608 . 2 (𝜑𝐴 ∈ ℝ)
32rexrd 11206 1 (𝜑𝐴 ∈ ℝ*)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2107  *cxr 11189  cz 12500
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2708
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3or 1089  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-rab 3409  df-v 3448  df-dif 3914  df-un 3916  df-in 3918  df-ss 3928  df-nul 4284  df-if 4488  df-sn 4588  df-pr 4590  df-op 4594  df-uni 4867  df-br 5107  df-iota 6449  df-fv 6505  df-ov 7361  df-xr 11194  df-neg 11389  df-z 12501
This theorem is referenced by: (None)
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