ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  rpxrd Unicode version

Theorem rpxrd 9273
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 9272 . 2  |-  ( ph  ->  A  e.  RR )
32rexrd 7634 1  |-  ( ph  ->  A  e.  RR* )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1445   RR*cxr 7618   RR+crp 9233
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077
This theorem depends on definitions:  df-bi 116  df-tru 1299  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224  df-rab 2379  df-v 2635  df-un 3017  df-in 3019  df-ss 3026  df-xr 7623  df-rp 9234
This theorem is referenced by:  ssblex  12217  metequiv2  12282  metss2lem  12283  metcnp  12294  metcnpi3  12299
  Copyright terms: Public domain W3C validator