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Theorem ltrelpi 6883
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 6866 . 2  |-  <N  =  (  _E  i^i  ( N.  X.  N. ) )
2 inss2 3221 . 2  |-  (  _E 
i^i  ( N.  X.  N. ) )  C_  ( N.  X.  N. )
31, 2eqsstri 3056 1  |-  <N  C_  ( N.  X.  N. )
Colors of variables: wff set class
Syntax hints:    i^i cin 2998    C_ wss 2999    _E cep 4114    X. cxp 4436   N.cnpi 6831    <N clti 6834
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-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-in 3005  df-ss 3012  df-lti 6866
This theorem is referenced by:  ltsonq  6957  caucvgprlemk  7224  caucvgprlem1  7238  caucvgprlem2  7239  caucvgprprlemk  7242  caucvgprprlemval  7247  caucvgprprlem1  7268  caucvgprprlem2  7269  ltrenn  7392
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