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Theorem lerel 8905
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 8904 . 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    <_ cle 8884
This theorem is referenced by:  dfle2  10497  dflt2  10498  ledm  14362  lern  14363  lefld  14364  letsr  14365  dvle  19370  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-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-dif 3168  df-in 3172  df-ss 3179  df-opab 4094  df-xp 4711  df-rel 4712  df-le 8889
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