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Theorem oveqi 6061
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 6054 . 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 1649  (class class class)co 6048
This theorem is referenced by:  oveq123i  6062  cantnfval2  7588  vdwap1  13308  vdwlem12  13323  prdsdsval3  13670  oppchom  13904  yonedalem21  14333  yonedalem22  14338  mndprop  14686  issubm  14711  frmdadd  14763  grpprop  14787  oppgplus  15108  ablprop  15386  rngpropd  15658  crngpropd  15659  rngprop  15660  opprmul  15694  opprrngb  15700  mulgass3  15705  rngidpropd  15763  invrpropd  15766  drngprop  15809  subrgpropd  15865  rhmpropd  15866  lidlacl  16247  lidlmcl  16251  lidlrsppropd  16264  crngridl  16272  psradd  16409  ressmpladd  16483  ressmplmul  16484  ressmplvsca  16485  ressply1add  16587  ressply1mul  16588  ressply1vsca  16589  ply1coe  16647  xpsdsval  18372  blres  18422  nmfval2  18599  nmval2  18600  cncfmet  18899  minveclem2  19288  minveclem3b  19290  minveclem4  19294  minveclem6  19296  ply1divalg2  20022  issubgoi  21859  ghgrplem2  21916  nvm  22083  xrge0pluscn  24287  esumpfinvallem  24425  equivbnd2  26399  ismtyres  26415  iccbnd  26447  exidreslem  26450  iscrngo2  26506  mendplusgfval  27369  toycom  29467
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-rex 2680  df-uni 3984  df-br 4181  df-iota 5385  df-fv 5429  df-ov 6051
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