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Theorem ltrelpi 9296
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 9282 . 2  |-  <N  =  (  _E  i^i  ( N.  X.  N. ) )
2 inss2 3659 . 2  |-  (  _E 
i^i  ( N.  X.  N. ) )  C_  ( N.  X.  N. )
31, 2eqsstri 3471 1  |-  <N  C_  ( N.  X.  N. )
Colors of variables: wff setvar class
Syntax hints:    i^i cin 3412    C_ wss 3413    _E cep 4731    X. cxp 4820   N.cnpi 9251    <N clti 9254
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380
This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-v 3060  df-in 3420  df-ss 3427  df-lti 9282
This theorem is referenced by:  ltapi  9310  ltmpi  9311  nlt1pi  9313  indpi  9314  ordpipq  9349  ltsonq  9376  archnq  9387
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