Theorem prpssnq 9389

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.

Step	Hyp	Ref	Expression
1		elnpi 9387	. 2
2		simpl3 1001	. 2
3	1, 2	sylbi 195	1

Syntax hints:  ->wi 4  /\wa 369  /\w3a 973  A.wal 1393  e.wcel 1818  A.wral 2807  E.wrex 2808  cvv 3109  C.wpss 3476  c0 3784   class class class wbr 4452  cnq 9251  cltq 9257  cnp 9258

This theorem is referenced by:  elprnq  9390  npomex  9395  genpnnp  9404  prlem934  9432  ltexprlem2  9436  reclem2pr  9447  suplem1pr  9451  wuncn  9568

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-v 3111  df-in 3482  df-ss 3489  df-pss 3491  df-np 9380