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Theorem enqex 8804
 Description: The equivalence relation for positive fractions exists. (Contributed by NM, 3-Sep-1995.) (New usage is discouraged.)
Assertion
Ref Expression
enqex

Proof of Theorem enqex
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 niex 8763 . . . 4
21, 1xpex 4993 . . 3
32, 2xpex 4993 . 2
4 df-enq 8793 . . 3
5 opabssxp 4953 . . 3
64, 5eqsstri 3380 . 2
73, 6ssexi 4351 1
 Colors of variables: wff set class Syntax hints:   wa 360  wex 1551   wceq 1653   wcel 1726  cvv 2958  cop 3819  copab 4268   cxp 4879  (class class class)co 6084  cnpi 8724   cmi 8726   ceq 8731 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pow 4380  ax-pr 4406  ax-un 4704  ax-inf2 7599 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3or 938  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-sbc 3164  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-pss 3338  df-nul 3631  df-if 3742  df-pw 3803  df-sn 3822  df-pr 3823  df-tp 3824  df-op 3825  df-uni 4018  df-br 4216  df-opab 4270  df-tr 4306  df-eprel 4497  df-po 4506  df-so 4507  df-fr 4544  df-we 4546  df-ord 4587  df-on 4588  df-lim 4589  df-suc 4590  df-om 4849  df-xp 4887  df-ni 8754  df-enq 8793
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