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Theorem ltrelre 9014
 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 9008 . 2
2 opabssxp 4953 . 2
31, 2eqsstri 3380 1
 Colors of variables: wff set class Syntax hints:   wa 360  wex 1551   wceq 1653   wcel 1726   wss 3322  cop 3819   class class class wbr 4215  copab 4268   cxp 4879  c0r 8748   cltr 8753  cr 8994   cltrr 8999 This theorem is referenced by:  ltresr  9020 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-in 3329  df-ss 3336  df-opab 4270  df-xp 4887  df-lt 9008
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