Theorem zxrd 46187

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

Hypothesis

Ref	Expression
zxrd.1	⊢ (𝜑 → 𝐴 ∈ ℤ)

Assertion

Ref	Expression
zxrd	⊢ (𝜑 → 𝐴 ∈ ℝ*)

Proof of Theorem zxrd

Step	Hyp	Ref	Expression
1		zxrd.1	. . 3 ⊢ (𝜑 → 𝐴 ∈ ℤ)
2	1	zred 12695	. 2 ⊢ (𝜑 → 𝐴 ∈ ℝ)
3	2	rexrd 11254	1 ⊢ (𝜑 → 𝐴 ∈ ℝ*)

Syntax hints:   → wi 4   ∈ wcel 2143  ℝ^*cxr 11237  ℤcz 12586

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3or 1104  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-rab 3417  df-v 3457  df-dif 3908  df-un 3910  df-ss 3922  df-nul 4287  df-if 4488  df-sn 4590  df-pr 4592  df-op 4596  df-uni 4873  df-br 5110  df-iota 6492  df-fv 6544  df-ov 7413  df-xr 11242  df-neg 11439  df-z 12587

This theorem is referenced by:  hoicvr  47282