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Theorem lerel 9075
Description: 'Less or equal to' is a relation. (Contributed by FL, 2-Aug-2009.) (Revised by Mario Carneiro, 28-Apr-2015.)
Assertion
Ref Expression
lerel  |-  Rel  <_

Proof of Theorem lerel
StepHypRef Expression
1 lerelxr 9074 . 2  |-  <_  C_  ( RR*  X.  RR* )
2 relxp 4923 . 2  |-  Rel  ( RR*  X.  RR* )
3 relss 4903 . 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 3263    X. cxp 4816   Rel wrel 4823   RR*cxr 9052    <_ cle 9054
This theorem is referenced by:  dfle2  10672  dflt2  10673  ledm  14596  lern  14597  lefld  14598  letsr  14599  dvle  19758  gtiso  23929
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-v 2901  df-dif 3266  df-in 3270  df-ss 3277  df-opab 4208  df-xp 4824  df-rel 4825  df-le 9059
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