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Theorem fnovpop 25038
 Description: Representation of an operation class abstraction in terms of its values. (A version of fnov 5952 adapted to partial operations.) (Contributed by FL, 18-Apr-2010.) (Revised by Mario Carneiro, 10-Sep-2015.)
Assertion
Ref Expression
fnovpop
Distinct variable groups:   ,,,   ,,,

Proof of Theorem fnovpop
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dffn5 5568 . 2
2 df-mpt 4079 . . . 4
3 fveq2 5525 . . . . . . 7
4 df-ov 5861 . . . . . . 7
53, 4syl6eqr 2333 . . . . . 6
65eqeq2d 2294 . . . . 5
76dfoprab4pop 25037 . . . 4
82, 7syl5eq 2327 . . 3
98eqeq2d 2294 . 2
101, 9syl5bb 248 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358   wceq 1623   wcel 1684  cop 3643  copab 4076   cmpt 4077   wrel 4694   wfn 5250  cfv 5255  (class class class)co 5858  coprab 5859 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-sbc 2992  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-opab 4078  df-mpt 4079  df-id 4309  df-xp 4695  df-rel 4696  df-cnv 4697  df-co 4698  df-dm 4699  df-iota 5219  df-fun 5257  df-fn 5258  df-fv 5263  df-ov 5861  df-oprab 5862
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