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Theorem ltrelre 9532
Description: 'Less than' is a relation on real numbers. (Contributed by NM, 22-Feb-1996.) (New usage is discouraged.)
Assertion
Ref Expression
ltrelre

Proof of Theorem ltrelre
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-lt 9526 . 2
2 opabssxp 5079 . 2
31, 2eqsstri 3533 1
Colors of variables: wff setvar class
Syntax hints:  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818  C_wss 3475  <.cop 4035   class class class wbr 4452  {copab 4509  X.cxp 5002   c0r 9265   cltr 9270   cr 9512   cltrr 9517
This theorem is referenced by:  ltresr  9538
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-in 3482  df-ss 3489  df-opab 4511  df-xp 5010  df-lt 9526
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