Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  ovig Unicode version

Theorem ovig 5622
 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 901 . 2
2 eleq1 2100 . . . . . 6
3 eleq1 2100 . . . . . 6
42, 3bi2anan9 538 . . . . 5
543adant3 924 . . . 4
6 ovig.1 . . . 4
75, 6anbi12d 442 . . 3
8 ovig.2 . . . 4
9 moanimv 1975 . . . 4
108, 9mpbir 134 . . 3
11 ovig.3 . . 3
127, 10, 11ovigg 5621 . 2
131, 12mpand 405 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98   w3a 885   wceq 1243   wcel 1393  wmo 1901  (class class class)co 5512  coprab 5513 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-pow 3927  ax-pr 3944 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-sbc 2765  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-op 3384  df-uni 3581  df-br 3765  df-opab 3819  df-id 4030  df-xp 4351  df-rel 4352  df-cnv 4353  df-co 4354  df-dm 4355  df-iota 4867  df-fun 4904  df-fv 4910  df-ov 5515  df-oprab 5516 This theorem is referenced by:  th3q  6211  addnnnq0  6547  mulnnnq0  6548  addsrpr  6830  mulsrpr  6831
 Copyright terms: Public domain W3C validator