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Theorem ltrelnq 9627
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 9619 . 2 <Q = ( <pQ ∩ (Q × Q))
2 inss2 3796 . 2 ( <pQ ∩ (Q × Q)) ⊆ (Q × Q)
31, 2eqsstri 3598 1 <Q ⊆ (Q × Q)
Colors of variables: wff setvar class
Syntax hints:  cin 3539  wss 3540   × cxp 5036   <pQ cltpq 9551  Qcnq 9553   <Q cltq 9559
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590
This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-in 3547  df-ss 3554  df-ltnq 9619
This theorem is referenced by:  lterpq  9671  ltanq  9672  ltmnq  9673  ltexnq  9676  ltbtwnnq  9679  ltrnq  9680  prcdnq  9694  prnmadd  9698  genpcd  9707  nqpr  9715  1idpr  9730  prlem934  9734  ltexprlem4  9740  prlem936  9748  reclem2pr  9749  reclem3pr  9750  reclem4pr  9751
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