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Theorem ltrelpi 7155
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 7138 . 2 <N = ( E ∩ (N × N))
2 inss2 3301 . 2 ( E ∩ (N × N)) ⊆ (N × N)
31, 2eqsstri 3133 1 <N ⊆ (N × N)
Colors of variables: wff set class
Syntax hints:  cin 3074  wss 3075   E cep 4216   × cxp 4544  Ncnpi 7103   <N clti 7106
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2691  df-in 3081  df-ss 3088  df-lti 7138
This theorem is referenced by:  ltsonq  7229  caucvgprlemk  7496  caucvgprlem1  7510  caucvgprlem2  7511  caucvgprprlemk  7514  caucvgprprlemval  7519  caucvgprprlem1  7540  caucvgprprlem2  7541  ltrenn  7686
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