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Theorem ltrelpi 10300
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 10286 . 2 <N = ( E ∩ (N × N))
2 inss2 4156 . 2 ( E ∩ (N × N)) ⊆ (N × N)
31, 2eqsstri 3949 1 <N ⊆ (N × N)
Colors of variables: wff setvar class
Syntax hints:  cin 3880  wss 3881   E cep 5429   × cxp 5517  Ncnpi 10255   <N clti 10258
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770
This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1541  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-rab 3115  df-v 3443  df-in 3888  df-ss 3898  df-lti 10286
This theorem is referenced by:  ltapi  10314  ltmpi  10315  nlt1pi  10317  indpi  10318  ordpipq  10353  ltsonq  10380  archnq  10391
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