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Theorem ltrelsr 7539
 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 7531 . 2
2 opabssxp 4608 . 2
31, 2eqsstri 3124 1
 Colors of variables: wff set class Syntax hints:   wa 103   wceq 1331  wex 1468   wcel 1480   wss 3066  cop 3525   class class class wbr 3924  copab 3983   cxp 4532  (class class class)co 5767  cec 6420   cpp 7094   cltp 7096   cer 7097  cnr 7098   cltr 7104 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-in 3072  df-ss 3079  df-opab 3985  df-xp 4540  df-ltr 7531 This theorem is referenced by:  gt0srpr  7549  recexgt0sr  7574  addgt0sr  7576  mulgt0sr  7579  caucvgsrlemcl  7590  caucvgsrlemasr  7591  caucvgsrlemfv  7592  map2psrprg  7606  suplocsrlemb  7607  suplocsrlempr  7608  suplocsrlem  7609  suplocsr  7610  ltresr  7640  axpre-ltirr  7683  axpre-lttrn  7685
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