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Theorem ltrelnq 9700
Description: Positive fraction 'less than' is a relation on positive fractions. (Contributed by NM, 14-Feb-1996.) (Revised by Mario Carneiro, 27-Apr-2013.) (New usage is discouraged.)
Assertion
Ref Expression
ltrelnq <Q ⊆ (Q × Q)

Proof of Theorem ltrelnq
StepHypRef Expression
1 df-ltnq 9692 . 2 <Q = ( <pQ ∩ (Q × Q))
2 inss2 3817 . 2 ( <pQ ∩ (Q × Q)) ⊆ (Q × Q)
31, 2eqsstri 3619 1 <Q ⊆ (Q × Q)
Colors of variables: wff setvar class
Syntax hints:  cin 3558  wss 3559   × cxp 5077   <pQ cltpq 9624  Qcnq 9626   <Q cltq 9632
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-v 3191  df-in 3566  df-ss 3573  df-ltnq 9692
This theorem is referenced by:  lterpq  9744  ltanq  9745  ltmnq  9746  ltexnq  9749  ltbtwnnq  9752  ltrnq  9753  prcdnq  9767  prnmadd  9771  genpcd  9780  nqpr  9788  1idpr  9803  prlem934  9807  ltexprlem4  9813  prlem936  9821  reclem2pr  9822  reclem3pr  9823  reclem4pr  9824
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