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Theorem rpxr 8590
 Description: A positive real is an extended real. (Contributed by Mario Carneiro, 21-Aug-2015.)
Assertion
Ref Expression
rpxr (𝐴 ∈ ℝ+𝐴 ∈ ℝ*)

Proof of Theorem rpxr
StepHypRef Expression
1 rpre 8589 . 2 (𝐴 ∈ ℝ+𝐴 ∈ ℝ)
21rexrd 7075 1 (𝐴 ∈ ℝ+𝐴 ∈ ℝ*)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∈ wcel 1393  ℝ*cxr 7059  ℝ+crp 8583 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rab 2315  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-xr 7064  df-rp 8584 This theorem is referenced by: (None)
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