Theorem zxrd 44826

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 12691	. 2 ⊢ (𝜑 → 𝐴 ∈ ℝ)
3	2	rexrd 11289	1 ⊢ (𝜑 → 𝐴 ∈ ℝ*)

Syntax hints:   → wi 4   ∈ wcel 2099  ℝ^*cxr 11272  ℤcz 12583

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2699

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-3or 1086  df-3an 1087  df-tru 1537  df-fal 1547  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-rab 3429  df-v 3472  df-dif 3948  df-un 3950  df-in 3952  df-ss 3962  df-nul 4320  df-if 4526  df-sn 4626  df-pr 4628  df-op 4632  df-uni 4905  df-br 5144  df-iota 6495  df-fv 6551  df-ov 7418  df-xr 11277  df-neg 11472  df-z 12584

This theorem is referenced by: (None)