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Theorem ltrelsr 6823
 Description: Signed real 'less than' is a relation on signed reals. (Contributed by NM, 14-Feb-1996.)
Assertion
Ref Expression
ltrelsr

Proof of Theorem ltrelsr
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-ltr 6815 . 2
2 opabssxp 4414 . 2
31, 2eqsstri 2975 1
 Colors of variables: wff set class Syntax hints:   wa 97   wceq 1243  wex 1381   wcel 1393   wss 2917  cop 3378   class class class wbr 3764  copab 3817   cxp 4343  (class class class)co 5512  cec 6104   cpp 6391   cltp 6393   cer 6394  cnr 6395   cltr 6401 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-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-in 2924  df-ss 2931  df-opab 3819  df-xp 4351  df-ltr 6815 This theorem is referenced by:  gt0srpr  6833  recexgt0sr  6858  addgt0sr  6860  mulgt0sr  6862  caucvgsrlemcl  6873  caucvgsrlemasr  6874  caucvgsrlemfv  6875  ltresr  6915  axpre-ltirr  6956  axpre-lttrn  6958
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