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Theorem ltrel 7081
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 7080 . 2  |-  <  C_  ( RR*  X.  RR* )
2 relxp 4447 . 2  |-  Rel  ( RR*  X.  RR* )
3 relss 4427 . 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 2917    X. cxp 4343   Rel wrel 4350   RR*cxr 7059    < clt 7060
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-pr 3382  df-opab 3819  df-xp 4351  df-rel 4352  df-xr 7064  df-ltxr 7065
This theorem is referenced by: (None)
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