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

Theorem lenlti 9195
 Description: 'Less than or equal to' in terms of 'less than'. (Contributed by NM, 24-May-1999.)
Hypotheses
Ref Expression
lt.1
lt.2
Assertion
Ref Expression
lenlti

Proof of Theorem lenlti
StepHypRef Expression
1 lt.1 . 2
2 lt.2 . 2
3 lenlt 9156 . 2
41, 2, 3mp2an 655 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 178   wcel 1726   class class class wbr 4214  cr 8991   clt 9122   cle 9123 This theorem is referenced by:  ltnlei  9196  ltadd2i  9206  hashgt12el  11684  hashgt12el2  11685  georeclim  12651  geoisumr  12657  divalglem6  12920  konigsberg  21711  ballotlem4  24758 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pr 4405 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4215  df-opab 4269  df-xp 4886  df-cnv 4888  df-xr 9126  df-le 9128
 Copyright terms: Public domain W3C validator