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Theorem lerel 9601
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 9600 . 2  |-  <_  C_  ( RR*  X.  RR* )
2 relxp 5052 . 2  |-  Rel  ( RR*  X.  RR* )
3 relss 5032 . 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 3413    X. cxp 4940   Rel wrel 4947   RR*cxr 9577    <_ cle 9579
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-v 3060  df-dif 3416  df-in 3420  df-ss 3427  df-opab 4453  df-xp 4948  df-rel 4949  df-le 9584
This theorem is referenced by:  dfle2  11324  dflt2  11325  ledm  16070  lern  16071  lefld  16072  letsr  16073  dvle  22592  gtiso  27843
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