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Theorem ltrelpi 7273
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 7256 . 2  |-  <N  =  (  _E  i^i  ( N.  X.  N. ) )
2 inss2 3348 . 2  |-  (  _E 
i^i  ( N.  X.  N. ) )  C_  ( N.  X.  N. )
31, 2eqsstri 3179 1  |-  <N  C_  ( N.  X.  N. )
Colors of variables: wff set class
Syntax hints:    i^i cin 3120    C_ wss 3121    _E cep 4270    X. cxp 4607   N.cnpi 7221    <N clti 7224
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-in 3127  df-ss 3134  df-lti 7256
This theorem is referenced by:  ltsonq  7347  caucvgprlemk  7614  caucvgprlem1  7628  caucvgprlem2  7629  caucvgprprlemk  7632  caucvgprprlemval  7637  caucvgprprlem1  7658  caucvgprprlem2  7659  ltrenn  7804
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