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Theorem lerel 9441
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 9440 . 2  |-  <_  C_  ( RR*  X.  RR* )
2 relxp 4947 . 2  |-  Rel  ( RR*  X.  RR* )
3 relss 4927 . 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 3328    X. cxp 4838   Rel wrel 4845   RR*cxr 9417    <_ cle 9419
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-v 2974  df-dif 3331  df-in 3335  df-ss 3342  df-opab 4351  df-xp 4846  df-rel 4847  df-le 9424
This theorem is referenced by:  dfle2  11124  dflt2  11125  ledm  15394  lern  15395  lefld  15396  letsr  15397  dvle  21479  gtiso  25996
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