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Theorem ltrelsr 8936
 Description: Signed real 'less than' is a relation on signed reals. (Contributed by NM, 14-Feb-1996.) (New usage is discouraged.)
Assertion
Ref Expression
ltrelsr

Proof of Theorem ltrelsr
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-ltr 8928 . 2
2 opabssxp 4942 . 2
31, 2eqsstri 3370 1
 Colors of variables: wff set class Syntax hints:   wa 359  wex 1550   wceq 1652   wcel 1725   wss 3312  cop 3809   class class class wbr 4204  copab 4257   cxp 4868  (class class class)co 6073  cec 6895   cpp 8726   cltp 8728   cer 8731  cnr 8732   cltr 8738 This theorem is referenced by:  ltsrpr  8942  ltasr  8965  recexsrlem  8968  addgt0sr  8969  mulgt0sr  8970  map2psrpr  8975  supsrlem  8976  supsr  8977  ltresr  9005  axpre-lttrn  9031 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-in 3319  df-ss 3326  df-opab 4259  df-xp 4876  df-ltr 8928
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