ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  ltrelpi GIF version

Theorem ltrelpi 7326
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 7309 . 2 <N = ( E ∩ (N × N))
2 inss2 3358 . 2 ( E ∩ (N × N)) ⊆ (N × N)
31, 2eqsstri 3189 1 <N ⊆ (N × N)
Colors of variables: wff set class
Syntax hints:  cin 3130  wss 3131   E cep 4289   × cxp 4626  Ncnpi 7274   <N clti 7277
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2741  df-in 3137  df-ss 3144  df-lti 7309
This theorem is referenced by:  ltsonq  7400  caucvgprlemk  7667  caucvgprlem1  7681  caucvgprlem2  7682  caucvgprprlemk  7685  caucvgprprlemval  7690  caucvgprprlem1  7711  caucvgprprlem2  7712  ltrenn  7857
  Copyright terms: Public domain W3C validator