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

Theorem ovigg 5968
 Description: The value of an operation class abstraction. Compare ovig 5969. 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 5934 . 2
3 df-ov 5861 . . . 4
4 ovigg.5 . . . . 5
54fveq1i 5526 . . . 4
63, 5eqtri 2303 . . 3
7 ovigg.4 . . . . 5
87funoprab 5944 . . . 4
9 funopfv 5562 . . . 4
108, 9ax-mp 8 . . 3
116, 10syl5eq 2327 . 2
122, 11syl6bir 220 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   w3a 934   wceq 1623   wcel 1684  wmo 2144  cop 3643   wfun 5249  cfv 5255  (class class class)co 5858  coprab 5859 This theorem is referenced by:  ovig  5969  cmp2morp  25958 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-id 4309  df-xp 4695  df-rel 4696  df-cnv 4697  df-co 4698  df-dm 4699  df-iota 5219  df-fun 5257  df-fv 5263  df-ov 5861  df-oprab 5862
 Copyright terms: Public domain W3C validator