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Theorem ovigg 6297
 Description: The value of an operation class abstraction. Compare ovig 6298. 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 6263 . 2
3 df-ov 6179 . . . 4
4 ovigg.5 . . . . 5
54fveq1i 5776 . . . 4
63, 5eqtri 2478 . . 3
7 ovigg.4 . . . . 5
87funoprab 6276 . . . 4
9 funopfv 5816 . . . 4
108, 9ax-mp 5 . . 3
116, 10syl5eq 2502 . 2
122, 11syl6bir 229 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   w3a 965   wceq 1370   wcel 1757  wmo 2260  cop 3967   wfun 5496  cfv 5502  (class class class)co 6176  coprab 6177 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1709  ax-7 1729  ax-9 1761  ax-10 1776  ax-11 1781  ax-12 1793  ax-13 1944  ax-ext 2429  ax-sep 4497  ax-nul 4505  ax-pr 4615 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1702  df-eu 2263  df-mo 2264  df-clab 2436  df-cleq 2442  df-clel 2445  df-nfc 2598  df-ne 2643  df-ral 2797  df-rex 2798  df-rab 2801  df-v 3056  df-sbc 3271  df-dif 3415  df-un 3417  df-in 3419  df-ss 3426  df-nul 3722  df-if 3876  df-sn 3962  df-pr 3964  df-op 3968  df-uni 4176  df-br 4377  df-opab 4435  df-id 4720  df-xp 4930  df-rel 4931  df-cnv 4932  df-co 4933  df-dm 4934  df-iota 5465  df-fun 5504  df-fv 5510  df-ov 6179  df-oprab 6180 This theorem is referenced by:  ovig  6298  joinval  15263  meetval  15277
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