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Theorem elrp 8585
 Description: Membership in the set of positive reals. (Contributed by NM, 27-Oct-2007.)
Assertion
Ref Expression
elrp

Proof of Theorem elrp
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 breq2 3768 . 2
2 df-rp 8584 . 2
31, 2elrab2 2700 1
 Colors of variables: wff set class Syntax hints:   wa 97   wb 98   wcel 1393   class class class wbr 3764  cr 6888  cc0 6889   clt 7060  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-3an 887  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-sn 3381  df-pr 3382  df-op 3384  df-br 3765  df-rp 8584 This theorem is referenced by:  elrpii  8586  nnrp  8592  rpgt0  8594  rpregt0  8596  ralrp  8604  rexrp  8605  rpaddcl  8606  rpmulcl  8607  rpdivcl  8608  rpgecl  8611  rphalflt  8612  ge0p1rp  8614  rpnegap  8615  ltsubrp  8617  ltaddrp  8618  difrp  8619  elrpd  8620  iccdil  8866  icccntr  8868  expgt0  9288  sqrtdiv  9640  mulcn2  9833
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