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Theorem lerel 7821
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 7820 . 2  |-  <_  C_  ( RR*  X.  RR* )
2 relxp 4643 . 2  |-  Rel  ( RR*  X.  RR* )
3 relss 4621 . 2  |-  (  <_  C_  ( RR*  X.  RR* )  ->  ( Rel  ( RR*  X. 
RR* )  ->  Rel  <_  ) )
41, 2, 3mp2 16 1  |-  Rel  <_
Colors of variables: wff set class
Syntax hints:    C_ wss 3066    X. cxp 4532   Rel wrel 4539   RR*cxr 7792    <_ cle 7794
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-dif 3068  df-in 3072  df-ss 3079  df-opab 3985  df-xp 4540  df-rel 4541  df-le 7799
This theorem is referenced by: (None)
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