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Theorem ltrelpi 9256
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 9242 . 2  |-  <N  =  (  _E  i^i  ( N.  X.  N. ) )
2 inss2 3712 . 2  |-  (  _E 
i^i  ( N.  X.  N. ) )  C_  ( N.  X.  N. )
31, 2eqsstri 3527 1  |-  <N  C_  ( N.  X.  N. )
Colors of variables: wff setvar class
Syntax hints:    i^i cin 3468    C_ wss 3469    _E cep 4782    X. cxp 4990   N.cnpi 9211    <N clti 9214
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1961  ax-ext 2438
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-clab 2446  df-cleq 2452  df-clel 2455  df-nfc 2610  df-v 3108  df-in 3476  df-ss 3483  df-lti 9242
This theorem is referenced by:  ltapi  9270  ltmpi  9271  nlt1pi  9273  indpi  9274  ordpipq  9309  ltsonq  9336  archnq  9347
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