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Theorem ltrelpi 9079
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 9065 . 2  |-  <N  =  (  _E  i^i  ( N.  X.  N. ) )
2 inss2 3592 . 2  |-  (  _E 
i^i  ( N.  X.  N. ) )  C_  ( N.  X.  N. )
31, 2eqsstri 3407 1  |-  <N  C_  ( N.  X.  N. )
Colors of variables: wff setvar class
Syntax hints:    i^i cin 3348    C_ wss 3349    _E cep 4651    X. cxp 4859   N.cnpi 9032    <N clti 9035
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2577  df-v 2995  df-in 3356  df-ss 3363  df-lti 9065
This theorem is referenced by:  ltapi  9093  ltmpi  9094  nlt1pi  9096  indpi  9097  ordpipq  9132  ltsonq  9159  archnq  9170
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