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Theorem prpssnq 8869
 Description: A positive real is a subset of the positive fractions. (Contributed by NM, 29-Feb-1996.) (Revised by Mario Carneiro, 11-May-2013.) (New usage is discouraged.)
Assertion
Ref Expression
prpssnq

Proof of Theorem prpssnq
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 elnpi 8867 . 2
2 simpl3 963 . 2
31, 2sylbi 189 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   w3a 937  wal 1550   wcel 1726  wral 2707  wrex 2708  cvv 2958   wpss 3323  c0 3630   class class class wbr 4214  cnq 8729   cltq 8735  cnp 8736 This theorem is referenced by:  elprnq  8870  npomex  8875  genpnnp  8884  prlem934  8912  ltexprlem2  8916  reclem2pr  8927  suplem1pr  8931  wuncn  9047 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-v 2960  df-in 3329  df-ss 3336  df-pss 3338  df-np 8860
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