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Theorem lerel 8889
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 8888 . 2  |-  <_  C_  ( RR*  X.  RR* )
2 relxp 4794 . 2  |-  Rel  ( RR*  X.  RR* )
3 relss 4775 . 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 3152    X. cxp 4687   Rel wrel 4694   RR*cxr 8866    <_ cle 8868
This theorem is referenced by:  dfle2  10481  dflt2  10482  ledm  14346  lern  14347  lefld  14348  letsr  14349  dvle  19354  gtiso  23241
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-dif 3155  df-in 3159  df-ss 3166  df-opab 4078  df-xp 4695  df-rel 4696  df-le 8873
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