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Theorem ltrelre 7641
 Description: 'Less than' is a relation on real numbers. (Contributed by NM, 22-Feb-1996.)
Assertion
Ref Expression
ltrelre

Proof of Theorem ltrelre
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-lt 7633 . 2
2 opabssxp 4613 . 2
31, 2eqsstri 3129 1
 Colors of variables: wff set class Syntax hints:   wa 103   wceq 1331  wex 1468   wcel 1480   wss 3071  cop 3530   class class class wbr 3929  copab 3988   cxp 4537  c0r 7106   cltr 7111  cr 7619   cltrr 7624 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 2121 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-in 3077  df-ss 3084  df-opab 3990  df-xp 4545  df-lt 7633 This theorem is referenced by:  ltresr  7647
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