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Theorem ltrelpi 8529
Description: Positive integer 'less than' is a relation on positive integers. (Contributed by NM, 8-Feb-1996.) (New usage is discouraged.)
Assertion
Ref Expression
ltrelpi  |-  <N  C_  ( N.  X.  N. )

Proof of Theorem ltrelpi
StepHypRef Expression
1 df-lti 8515 . 2  |-  <N  =  (  _E  i^i  ( N.  X.  N. ) )
2 inss2 3403 . 2  |-  (  _E 
i^i  ( N.  X.  N. ) )  C_  ( N.  X.  N. )
31, 2eqsstri 3221 1  |-  <N  C_  ( N.  X.  N. )
Colors of variables: wff set class
Syntax hints:    i^i cin 3164    C_ wss 3165    _E cep 4319    X. cxp 4703   N.cnpi 8482    <N clti 8485
This theorem is referenced by:  ltapi  8543  ltmpi  8544  nlt1pi  8546  indpi  8547  ordpipq  8582  ltsonq  8609  archnq  8620
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-in 3172  df-ss 3179  df-lti 8515
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