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Theorem ovig 6424
 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:   ,,,   ,,,   ,,,   ,,,   ,S,,   ,,,

Proof of Theorem ovig
StepHypRef Expression
1 3simpa 993 . 2
2 eleq1 2529 . . . . . 6
3 eleq1 2529 . . . . . 6
42, 3bi2anan9 873 . . . . 5
543adant3 1016 . . . 4
6 ovig.1 . . . 4
75, 6anbi12d 710 . . 3
8 ovig.2 . . . 4
9 moanimv 2352 . . . 4
108, 9mpbir 209 . . 3
11 ovig.3 . . 3
127, 10, 11ovigg 6423 . 2
131, 12mpand 675 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  /\w3a 973  =wceq 1395  e.wcel 1818  E*wmo 2283  (class class class)co 6296  {coprab 6297 This theorem is referenced by:  addsrpr  9473  mulsrpr  9474 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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