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Theorem ltrel 8903
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 8902 . 2  |-  <  C_  ( RR*  X.  RR* )
2 relxp 4810 . 2  |-  Rel  ( RR*  X.  RR* )
3 relss 4791 . 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 3165    X. cxp 4703   Rel wrel 4710   RR*cxr 8882    < clt 8883
This theorem is referenced by:  dflt2  10498  ballotlemimin  23080  gtiso  23256
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-un 3170  df-in 3172  df-ss 3179  df-pr 3660  df-opab 4094  df-xp 4711  df-rel 4712  df-xr 8887  df-ltxr 8888
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