Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  lerel Structured version   Unicode version

Theorem lerel 9134
 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

Proof of Theorem lerel
StepHypRef Expression
1 lerelxr 9133 . 2
2 relxp 4975 . 2
3 relss 4955 . 2
41, 2, 3mp2 9 1
 Colors of variables: wff set class Syntax hints:   wss 3312   cxp 4868   wrel 4875  cxr 9111   cle 9113 This theorem is referenced by:  dfle2  10732  dflt2  10733  ledm  14661  lern  14662  lefld  14663  letsr  14664  dvle  19883  gtiso  24080 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-dif 3315  df-in 3319  df-ss 3326  df-opab 4259  df-xp 4876  df-rel 4877  df-le 9118
 Copyright terms: Public domain W3C validator