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Theorem ltrelpi 6308
Description: Positive integer 'less than' is a relation on positive integers. (Contributed by NM, 8-Feb-1996.)
Assertion
Ref Expression
ltrelpi <N ⊆ (N × N)

Proof of Theorem ltrelpi
StepHypRef Expression
1 df-lti 6291 . 2 <N = ( E ∩ (N × N))
2 inss2 3152 . 2 ( E ∩ (N × N)) ⊆ (N × N)
31, 2eqsstri 2969 1 <N ⊆ (N × N)
Colors of variables: wff set class
Syntax hints:  cin 2910  wss 2911   E cep 4015   × cxp 4286  Ncnpi 6256   <N clti 6259
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-in 2918  df-ss 2925  df-lti 6291
This theorem is referenced by:  ltsonq  6382  caucvgprlemk  6636  caucvgprlem1  6650  caucvgprlem2  6651
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