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Theorem ltrelpi 6422
Description: Positive integer 'less than' is a relation on positive integers. (Contributed by NM, 8-Feb-1996.)
Assertion
Ref Expression
ltrelpi  |-  <N  C_  ( N.  X.  N. )

Proof of Theorem ltrelpi
StepHypRef Expression
1 df-lti 6405 . 2  |-  <N  =  (  _E  i^i  ( N.  X.  N. ) )
2 inss2 3158 . 2  |-  (  _E 
i^i  ( N.  X.  N. ) )  C_  ( N.  X.  N. )
31, 2eqsstri 2975 1  |-  <N  C_  ( N.  X.  N. )
Colors of variables: wff set class
Syntax hints:    i^i cin 2916    C_ wss 2917    _E cep 4024    X. cxp 4343   N.cnpi 6370    <N clti 6373
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-in 2924  df-ss 2931  df-lti 6405
This theorem is referenced by:  ltsonq  6496  caucvgprlemk  6763  caucvgprlem1  6777  caucvgprlem2  6778  caucvgprprlemk  6781  caucvgprprlemval  6786  caucvgprprlem1  6807  caucvgprprlem2  6808  ltrenn  6931
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