Mathbox for Glauco Siliprandi < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  zxrd Structured version   Visualization version   GIF version

Theorem zxrd 39995
 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 11520 . 2 (𝜑𝐴 ∈ ℝ)
32rexrd 10127 1 (𝜑𝐴 ∈ ℝ*)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 2030  ℝ*cxr 10111  ℤcz 11415 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3or 1055  df-3an 1056  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-rex 2947  df-rab 2950  df-v 3233  df-dif 3610  df-un 3612  df-in 3614  df-ss 3621  df-nul 3949  df-if 4120  df-sn 4211  df-pr 4213  df-op 4217  df-uni 4469  df-br 4686  df-iota 5889  df-fv 5934  df-ov 6693  df-xr 10116  df-neg 10307  df-z 11416 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator