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Theorem ltrel 9142
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 9141 . 2  |-  <  C_  ( RR*  X.  RR* )
2 relxp 4985 . 2  |-  Rel  ( RR*  X.  RR* )
3 relss 4965 . 2  |-  (  <  C_  ( RR*  X.  RR* )  ->  ( Rel  ( RR*  X. 
RR* )  ->  Rel  <  ) )
41, 2, 3mp2 9 1  |-  Rel  <
Colors of variables: wff set class
Syntax hints:    C_ wss 3322    X. cxp 4878   Rel wrel 4885   RR*cxr 9121    < clt 9122
This theorem is referenced by:  dflt2  10743  gtiso  24090  ballotlemimin  24765
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-3an 939  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-v 2960  df-un 3327  df-in 3329  df-ss 3336  df-pr 3823  df-opab 4269  df-xp 4886  df-rel 4887  df-xr 9126  df-ltxr 9127
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