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Theorem ovig 6437
 Description: The value of an operation class abstraction (weak version). (Unnecessary distinct variable restrictions were removed by David Abernethy, 19-Jun-2012.) (Contributed by NM, 14-Sep-1999.) (Revised by Mario Carneiro, 19-Dec-2013.)
Hypotheses
Ref Expression
ovig.1
ovig.2
ovig.3
Assertion
Ref Expression
ovig
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,
Allowed substitution hints:   (,,)   (,,)   (,,)

Proof of Theorem ovig
StepHypRef Expression
1 3simpa 1027 . 2
2 eleq1 2537 . . . . . 6
3 eleq1 2537 . . . . . 6
42, 3bi2anan9 890 . . . . 5
543adant3 1050 . . . 4
6 ovig.1 . . . 4
75, 6anbi12d 725 . . 3
8 ovig.2 . . . 4
9 moanimv 2380 . . . 4
108, 9mpbir 214 . . 3
11 ovig.3 . . 3
127, 10, 11ovigg 6436 . 2
131, 12mpand 689 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189   wa 376   w3a 1007   wceq 1452   wcel 1904  wmo 2320  (class class class)co 6308  coprab 6309 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-sep 4518  ax-nul 4527  ax-pr 4639 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-mo 2324  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3033  df-sbc 3256  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-uni 4191  df-br 4396  df-opab 4455  df-id 4754  df-xp 4845  df-rel 4846  df-cnv 4847  df-co 4848  df-dm 4849  df-iota 5553  df-fun 5591  df-fv 5597  df-ov 6311  df-oprab 6312 This theorem is referenced by:  addsrpr  9517  mulsrpr  9518
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