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Theorem ltrel 8887
Description: 'Less than' is a relation. (Contributed by NM, 14-Oct-2005.)
Assertion
Ref Expression
ltrel  |-  Rel  <

Proof of Theorem ltrel
StepHypRef Expression
1 ltrelxr 8886 . 2  |-  <  C_  ( RR*  X.  RR* )
2 relxp 4794 . 2  |-  Rel  ( RR*  X.  RR* )
3 relss 4775 . 2  |-  (  <  C_  ( RR*  X.  RR* )  ->  ( Rel  ( RR*  X. 
RR* )  ->  Rel  <  ) )
41, 2, 3mp2 17 1  |-  Rel  <
Colors of variables: wff set class
Syntax hints:    C_ wss 3152    X. cxp 4687   Rel wrel 4694   RR*cxr 8866    < clt 8867
This theorem is referenced by:  dflt2  10482  ballotlemimin  23064  gtiso  23241
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-un 3157  df-in 3159  df-ss 3166  df-pr 3647  df-opab 4078  df-xp 4695  df-rel 4696  df-xr 8871  df-ltxr 8872
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