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Theorem ltnlei 9726
 Description: 'Less than' in terms of 'less than or equal to'. (Contributed by NM, 11-Jul-2005.)
Hypotheses
Ref Expression
lt.1
lt.2
Assertion
Ref Expression
ltnlei

Proof of Theorem ltnlei
StepHypRef Expression
1 lt.2 . . 3
2 lt.1 . . 3
31, 2lenlti 9725 . 2
43con2bii 332 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  <->wb 184  e.wcel 1818   class class class wbr 4452   cr 9512   clt 9649   cle 9650 This theorem is referenced by:  letrii  9730  nn0ge2m1nn  10886  fzpreddisj  11758  hashnn0n0nn  12458  hashge2el2dif  12521  n2dvds1  14035  divalglem5  14055  divalglem6  14056  sadcadd  14108  strlemor1  14724  htpycc  21480  pco1  21515  pcohtpylem  21519  pcopt  21522  pcopt2  21523  pcoass  21524  pcorevlem  21526  vitalilem5  22021  vieta1lem2  22707  ppiltx  23451  ppiublem1  23477  chtub  23487  axlowdimlem16  24260  axlowdim  24264  spthispth  24575  rnlogblem  28015  ballotlem2  28427  subfacp1lem1  28623  subfacp1lem5  28628  fdc  30238  pellexlem6  30770  jm2.23  30938 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-xp 5010  df-cnv 5012  df-xr 9653  df-le 9655
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