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Theorem ovigg 6423
Description: The value of an operation class abstraction. Compare ovig 6424. 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:   , , ,   , , ,   , , ,   , , ,

Proof of Theorem ovigg
StepHypRef Expression
1 ovigg.1 . . 3
21eloprabga 6389 . 2
3 df-ov 6299 . . . 4
4 ovigg.5 . . . . 5
54fveq1i 5872 . . . 4
63, 5eqtri 2486 . . 3
7 ovigg.4 . . . . 5
87funoprab 6402 . . . 4
9 funopfv 5912 . . . 4
108, 9ax-mp 5 . . 3
116, 10syl5eq 2510 . 2
122, 11syl6bir 229 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\w3a 973  =wceq 1395  e.wcel 1818  E*wmo 2283  <.cop 4035  Funwfun 5587  `cfv 5593  (class class class)co 6296  {coprab 6297
This theorem is referenced by:  ovig  6424  joinval  15635  meetval  15649
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-id 4800  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-iota 5556  df-fun 5595  df-fv 5601  df-ov 6299  df-oprab 6300
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