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Theorem ltrelpi 9749
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 ⊆ (N × N)

Proof of Theorem ltrelpi
StepHypRef Expression
1 df-lti 9735 . 2 <N = ( E ∩ (N × N))
2 inss2 3867 . 2 ( E ∩ (N × N)) ⊆ (N × N)
31, 2eqsstri 3668 1 <N ⊆ (N × N)
Colors of variables: wff setvar class
Syntax hints:  cin 3606  wss 3607   E cep 5057   × cxp 5141  Ncnpi 9704   <N clti 9707
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-v 3233  df-in 3614  df-ss 3621  df-lti 9735
This theorem is referenced by:  ltapi  9763  ltmpi  9764  nlt1pi  9766  indpi  9767  ordpipq  9802  ltsonq  9829  archnq  9840
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