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Theorem lerel 9647
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 9646 . 2  |-  <_  C_  ( RR*  X.  RR* )
2 relxp 5108 . 2  |-  Rel  ( RR*  X.  RR* )
3 relss 5088 . 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 3476    X. cxp 4997   Rel wrel 5004   RR*cxr 9623    <_ cle 9625
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-v 3115  df-dif 3479  df-in 3483  df-ss 3490  df-opab 4506  df-xp 5005  df-rel 5006  df-le 9630
This theorem is referenced by:  dfle2  11349  dflt2  11350  ledm  15704  lern  15705  lefld  15706  letsr  15707  dvle  22140  gtiso  27188
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