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Theorem rpxrd 9654
Description: A positive real is an extended real. (Contributed by Mario Carneiro, 28-May-2016.)
Hypothesis
Ref Expression
rpred.1  |-  ( ph  ->  A  e.  RR+ )
Assertion
Ref Expression
rpxrd  |-  ( ph  ->  A  e.  RR* )

Proof of Theorem rpxrd
StepHypRef Expression
1 rpred.1 . . 3  |-  ( ph  ->  A  e.  RR+ )
21rpred 9653 . 2  |-  ( ph  ->  A  e.  RR )
32rexrd 7969 1  |-  ( ph  ->  A  e.  RR* )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 2141   RR*cxr 7953   RR+crp 9610
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 7958  df-rp 9611
This theorem is referenced by:  ssblex  13225  metequiv2  13290  metss2lem  13291  metcnp  13306  metcnpi3  13311
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