Theorem zxrd 42883

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 12355	. 2 ⊢ (𝜑 → 𝐴 ∈ ℝ)
3	2	rexrd 10956	1 ⊢ (𝜑 → 𝐴 ∈ ℝ*)

Syntax hints:   → wi 4   ∈ wcel 2108  ℝ^*cxr 10939  ℤcz 12249

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-3or 1086  df-3an 1087  df-tru 1542  df-fal 1552  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-rab 3072  df-v 3424  df-dif 3886  df-un 3888  df-in 3890  df-ss 3900  df-nul 4254  df-if 4457  df-sn 4559  df-pr 4561  df-op 4565  df-uni 4837  df-br 5071  df-iota 6376  df-fv 6426  df-ov 7258  df-xr 10944  df-neg 11138  df-z 12250

This theorem is referenced by: (None)