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Theorem nqex 9366
 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 9355 . 2
2 niex 9324 . . 3
32, 2xpex 6614 . 2
41, 3rabex2 4552 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wcel 1904  wral 2756  cvv 3031   class class class wbr 4395   cxp 4837  cfv 5589  c2nd 6811  cnpi 9287   clti 9290   ceq 9294  cnq 9295 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-8 1906  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-sep 4518  ax-nul 4527  ax-pow 4579  ax-pr 4639  ax-un 6602  ax-inf2 8164 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3or 1008  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-mo 2324  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3033  df-sbc 3256  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-pss 3406  df-nul 3723  df-if 3873  df-pw 3944  df-sn 3960  df-pr 3962  df-tp 3964  df-op 3966  df-uni 4191  df-br 4396  df-opab 4455  df-tr 4491  df-eprel 4750  df-po 4760  df-so 4761  df-fr 4798  df-we 4800  df-xp 4845  df-rel 4846  df-ord 5433  df-on 5434  df-lim 5435  df-suc 5436  df-om 6712  df-ni 9315  df-nq 9355 This theorem is referenced by:  npex  9429  elnp  9430  genpv  9442  genpdm  9445
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