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Theorem ovigg 5621
 Description: The value of an operation class abstraction. Compare ovig 5622. The condition is been removed. (Contributed by FL, 24-Mar-2007.) (Revised by Mario Carneiro, 19-Dec-2013.)
Hypotheses
Ref Expression
ovigg.1
ovigg.4
ovigg.5
Assertion
Ref Expression
ovigg
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,
Allowed substitution hints:   (,,)   (,,)   (,,)   (,,)   (,,)

Proof of Theorem ovigg
StepHypRef Expression
1 ovigg.1 . . 3
21eloprabga 5591 . 2
3 df-ov 5515 . . . 4
4 ovigg.5 . . . . 5
54fveq1i 5179 . . . 4
63, 5eqtri 2060 . . 3
7 ovigg.4 . . . . 5
87funoprab 5601 . . . 4
9 funopfv 5213 . . . 4
108, 9ax-mp 7 . . 3
116, 10syl5eq 2084 . 2
122, 11syl6bir 153 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98   w3a 885   wceq 1243   wcel 1393  wmo 1901  cop 3378   wfun 4896  cfv 4902  (class class class)co 5512  coprab 5513 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-pow 3927  ax-pr 3944 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-sbc 2765  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-op 3384  df-uni 3581  df-br 3765  df-opab 3819  df-id 4030  df-xp 4351  df-rel 4352  df-cnv 4353  df-co 4354  df-dm 4355  df-iota 4867  df-fun 4904  df-fv 4910  df-ov 5515  df-oprab 5516 This theorem is referenced by:  ovig  5622
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