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Theorem ltrel 7241
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 7240 . 2  |-  <  C_  ( RR*  X.  RR* )
2 relxp 4475 . 2  |-  Rel  ( RR*  X.  RR* )
3 relss 4453 . 2  |-  (  <  C_  ( RR*  X.  RR* )  ->  ( Rel  ( RR*  X. 
RR* )  ->  Rel  <  ) )
41, 2, 3mp2 16 1  |-  Rel  <
Colors of variables: wff set class
Syntax hints:    C_ wss 2974    X. cxp 4369   Rel wrel 4376   RR*cxr 7214    < clt 7215
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-pr 3413  df-opab 3848  df-xp 4377  df-rel 4378  df-xr 7219  df-ltxr 7220
This theorem is referenced by: (None)
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