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Theorem lerel 9694
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 9693 . 2  |-  <_  C_  ( RR*  X.  RR* )
2 relxp 4954 . 2  |-  Rel  ( RR*  X.  RR* )
3 relss 4934 . 2  |-  (  <_  C_  ( RR*  X.  RR* )  ->  ( Rel  ( RR*  X. 
RR* )  ->  Rel  <_  ) )
41, 2, 3mp2 9 1  |-  Rel  <_
Colors of variables: wff setvar class
Syntax hints:    C_ wss 3433    X. cxp 4844   Rel wrel 4851   RR*cxr 9670    <_ cle 9672
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052  ax-ext 2398
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2406  df-cleq 2412  df-clel 2415  df-nfc 2570  df-v 3080  df-dif 3436  df-in 3440  df-ss 3447  df-opab 4477  df-xp 4852  df-rel 4853  df-le 9677
This theorem is referenced by:  dfle2  11442  dflt2  11443  ledm  16448  lern  16449  lefld  16450  letsr  16451  dvle  22936  gtiso  28262
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