Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  nqex Structured version   Unicode version

Theorem nqex 9207
 Description: The class of positive fractions exists. (Contributed by NM, 16-Aug-1995.) (Revised by Mario Carneiro, 27-Apr-2013.) (New usage is discouraged.)
Assertion
Ref Expression
nqex

Proof of Theorem nqex
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-nq 9196 . 2
2 niex 9165 . . . 4
32, 2xpex 6621 . . 3
43rabex 4554 . 2
51, 4eqeltri 2538 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wcel 1758  wral 2799  crab 2803  cvv 3078   class class class wbr 4403   cxp 4949  cfv 5529  c2nd 6689  cnpi 9126   clti 9129   ceq 9133  cnq 9134 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-8 1760  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432  ax-sep 4524  ax-nul 4532  ax-pow 4581  ax-pr 4642  ax-un 6485  ax-inf2 7962 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 966  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2266  df-mo 2267  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-ral 2804  df-rex 2805  df-rab 2808  df-v 3080  df-sbc 3295  df-dif 3442  df-un 3444  df-in 3446  df-ss 3453  df-pss 3455  df-nul 3749  df-if 3903  df-pw 3973  df-sn 3989  df-pr 3991  df-tp 3993  df-op 3995  df-uni 4203  df-br 4404  df-opab 4462  df-tr 4497  df-eprel 4743  df-po 4752  df-so 4753  df-fr 4790  df-we 4792  df-ord 4833  df-on 4834  df-lim 4835  df-suc 4836  df-xp 4957  df-om 6590  df-ni 9156  df-nq 9196 This theorem is referenced by:  npex  9270  elnp  9271  genpv  9283  genpdm  9286
 Copyright terms: Public domain W3C validator