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

Theorem zxrd 44673
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 12664 . 2 (𝜑𝐴 ∈ ℝ)
32rexrd 11262 1 (𝜑𝐴 ∈ ℝ*)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2098  *cxr 11245  cz 12556
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3or 1085  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-rab 3425  df-v 3468  df-dif 3944  df-un 3946  df-in 3948  df-ss 3958  df-nul 4316  df-if 4522  df-sn 4622  df-pr 4624  df-op 4628  df-uni 4901  df-br 5140  df-iota 6486  df-fv 6542  df-ov 7405  df-xr 11250  df-neg 11445  df-z 12557
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator