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Theorem rpxrd 9647
Description: A positive real is an extended real. (Contributed by Mario Carneiro, 28-May-2016.)
Hypothesis
Ref Expression
rpred.1 (𝜑𝐴 ∈ ℝ+)
Assertion
Ref Expression
rpxrd (𝜑𝐴 ∈ ℝ*)

Proof of Theorem rpxrd
StepHypRef Expression
1 rpred.1 . . 3 (𝜑𝐴 ∈ ℝ+)
21rpred 9646 . 2 (𝜑𝐴 ∈ ℝ)
32rexrd 7962 1 (𝜑𝐴 ∈ ℝ*)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 2141  *cxr 7946  +crp 9603
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-rab 2457  df-v 2732  df-un 3125  df-in 3127  df-ss 3134  df-xr 7951  df-rp 9604
This theorem is referenced by:  ssblex  13190  metequiv2  13255  metss2lem  13256  metcnp  13271  metcnpi3  13276
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