ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  lerel Unicode version

Theorem lerel 7548
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 7547 . 2  |-  <_  C_  ( RR*  X.  RR* )
2 relxp 4547 . 2  |-  Rel  ( RR*  X.  RR* )
3 relss 4525 . 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 2999    X. cxp 4436   Rel wrel 4443   RR*cxr 7519    <_ cle 7521
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-dif 3001  df-in 3005  df-ss 3012  df-opab 3900  df-xp 4444  df-rel 4445  df-le 7526
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator