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Theorem ltrelnq 8795
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 8787 . 2  |-  <Q  =  (  <pQ  i^i  ( Q.  X.  Q. ) )
2 inss2 3554 . 2  |-  (  <pQ  i^i  ( Q.  X.  Q. ) )  C_  ( Q.  X.  Q. )
31, 2eqsstri 3370 1  |-  <Q  C_  ( Q.  X.  Q. )
Colors of variables: wff set class
Syntax hints:    i^i cin 3311    C_ wss 3312    X. cxp 4868    <pQ cltpq 8717   Q.cnq 8719    <Q cltq 8725
This theorem is referenced by:  lterpq  8839  ltanq  8840  ltmnq  8841  ltexnq  8844  ltbtwnnq  8847  ltrnq  8848  prcdnq  8862  prnmadd  8866  genpcd  8875  nqpr  8883  1idpr  8898  prlem934  8902  ltexprlem4  8908  prlem936  8916  reclem2pr  8917  reclem3pr  8918  reclem4pr  8919
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-in 3319  df-ss 3326  df-ltnq 8787
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