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Theorem ltrelnq 9215
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  C_  ( Q.  X.  Q. )

Proof of Theorem ltrelnq
StepHypRef Expression
1 df-ltnq 9207 . 2  |-  <Q  =  (  <pQ  i^i  ( Q.  X.  Q. ) )
2 inss2 3633 . 2  |-  (  <pQ  i^i  ( Q.  X.  Q. ) )  C_  ( Q.  X.  Q. )
31, 2eqsstri 3447 1  |-  <Q  C_  ( Q.  X.  Q. )
Colors of variables: wff setvar class
Syntax hints:    i^i cin 3388    C_ wss 3389    X. cxp 4911    <pQ cltpq 9139   Q.cnq 9141    <Q cltq 9147
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1626  ax-4 1639  ax-5 1712  ax-6 1755  ax-7 1798  ax-10 1845  ax-11 1850  ax-12 1862  ax-13 2006  ax-ext 2360
This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1402  df-ex 1621  df-nf 1625  df-sb 1748  df-clab 2368  df-cleq 2374  df-clel 2377  df-nfc 2532  df-v 3036  df-in 3396  df-ss 3403  df-ltnq 9207
This theorem is referenced by:  lterpq  9259  ltanq  9260  ltmnq  9261  ltexnq  9264  ltbtwnnq  9267  ltrnq  9268  prcdnq  9282  prnmadd  9286  genpcd  9295  nqpr  9303  1idpr  9318  prlem934  9322  ltexprlem4  9328  prlem936  9336  reclem2pr  9337  reclem3pr  9338  reclem4pr  9339
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