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Theorem oveqi 6094
Description: Equality inference for operation value. (Contributed by NM, 24-Nov-2007.)
Hypothesis
Ref Expression
oveq1i.1  |-  A  =  B
Assertion
Ref Expression
oveqi  |-  ( C A D )  =  ( C B D )

Proof of Theorem oveqi
StepHypRef Expression
1 oveq1i.1 . 2  |-  A  =  B
2 oveq 6087 . 2  |-  ( A  =  B  ->  ( C A D )  =  ( C B D ) )
31, 2ax-mp 8 1  |-  ( C A D )  =  ( C B D )
Colors of variables: wff set class
Syntax hints:    = wceq 1652  (class class class)co 6081
This theorem is referenced by:  oveq123i  6095  cantnfval2  7624  vdwap1  13345  vdwlem12  13360  prdsdsval3  13707  oppchom  13941  yonedalem21  14370  yonedalem22  14375  mndprop  14723  issubm  14748  frmdadd  14800  grpprop  14824  oppgplus  15145  ablprop  15423  rngpropd  15695  crngpropd  15696  rngprop  15697  opprmul  15731  opprrngb  15737  mulgass3  15742  rngidpropd  15800  invrpropd  15803  drngprop  15846  subrgpropd  15902  rhmpropd  15903  lidlacl  16284  lidlmcl  16288  lidlrsppropd  16301  crngridl  16309  psradd  16446  ressmpladd  16520  ressmplmul  16521  ressmplvsca  16522  ressply1add  16624  ressply1mul  16625  ressply1vsca  16626  ply1coe  16684  xpsdsval  18411  blres  18461  nmfval2  18638  nmval2  18639  cncfmet  18938  minveclem2  19327  minveclem3b  19329  minveclem4  19333  minveclem6  19335  ply1divalg2  20061  issubgoi  21898  ghgrplem2  21955  nvm  22122  xrge0pluscn  24326  esumpfinvallem  24464  equivbnd2  26501  ismtyres  26517  iccbnd  26549  exidreslem  26552  iscrngo2  26608  mendplusgfval  27470  toycom  29770
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rex 2711  df-uni 4016  df-br 4213  df-iota 5418  df-fv 5462  df-ov 6084
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