Theorem zxrd 45902

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 12627	. 2 ⊢ (𝜑 → 𝐴 ∈ ℝ)
3	2	rexrd 11189	1 ⊢ (𝜑 → 𝐴 ∈ ℝ*)

Syntax hints:   → wi 4   ∈ wcel 2114  ℝ^*cxr 11172  ℤcz 12518

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3or 1088  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-rab 3391  df-v 3432  df-dif 3893  df-un 3895  df-ss 3907  df-nul 4275  df-if 4468  df-sn 4569  df-pr 4571  df-op 4575  df-uni 4852  df-br 5087  df-iota 6449  df-fv 6501  df-ov 7364  df-xr 11177  df-neg 11374  df-z 12519

This theorem is referenced by:  hoicvr  46997