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Theorem ltrelre 6909
 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 6902 . 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  c0r 6396   cltr 6401  cr 6888   cltrr 6893 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-lt 6902 This theorem is referenced by:  ltresr  6915
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