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Theorem ltrelpi 6576
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 6559 . 2  |-  <N  =  (  _E  i^i  ( N.  X.  N. ) )
2 inss2 3194 . 2  |-  (  _E 
i^i  ( N.  X.  N. ) )  C_  ( N.  X.  N. )
31, 2eqsstri 3030 1  |-  <N  C_  ( N.  X.  N. )
Colors of variables: wff set class
Syntax hints:    i^i cin 2973    C_ wss 2974    _E cep 4050    X. cxp 4369   N.cnpi 6524    <N clti 6527
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 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-in 2980  df-ss 2987  df-lti 6559
This theorem is referenced by:  ltsonq  6650  caucvgprlemk  6917  caucvgprlem1  6931  caucvgprlem2  6932  caucvgprprlemk  6935  caucvgprprlemval  6940  caucvgprprlem1  6961  caucvgprprlem2  6962  ltrenn  7085
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