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Theorem imaeq1i 5161
Description: Equality theorem for image. (Contributed by NM, 21-Dec-2008.)
Hypothesis
Ref Expression
imaeq1i.1  |-  A  =  B
Assertion
Ref Expression
imaeq1i  |-  ( A
" C )  =  ( B " C
)

Proof of Theorem imaeq1i
StepHypRef Expression
1 imaeq1i.1 . 2  |-  A  =  B
2 imaeq1 5159 . 2  |-  ( A  =  B  ->  ( A " C )  =  ( B " C
) )
31, 2ax-mp 5 1  |-  ( A
" C )  =  ( B " C
)
Colors of variables: wff setvar class
Syntax hints:    = wceq 1369   "cima 4838
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2419
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rab 2719  df-v 2969  df-dif 3326  df-un 3328  df-in 3330  df-ss 3337  df-nul 3633  df-if 3787  df-sn 3873  df-pr 3875  df-op 3879  df-br 4288  df-opab 4346  df-cnv 4843  df-dm 4845  df-rn 4846  df-res 4847  df-ima 4848
This theorem is referenced by:  mptpreima  5326  isarep2  5493  suppun  6704  supp0cosupp0  6723  imacosupp  6724  fsuppun  7631  fsuppcolem  7642  marypha2lem4  7680  dfoi  7717  mapfienOLD  7919  r1limg  7970  isf34lem3  8536  compss  8537  fpwwe2lem13  8801  infmsup  10300  gsumval3OLD  16373  gsumzf1o  16382  gsumzf1oOLD  16385  gsumzaddlemOLD  16401  dprdfidOLD  16502  funsnfsupOLD  17645  ssidcn  18834  cnco  18845  qtopres  19246  idqtop  19254  qtopcn  19262  mbfid  21089  mbfres  21097  cncombf  21111  dvlog  22071  efopnlem2  22077  disjpreima  25879  imadifxp  25890  rinvf1o  25900  mbfmcst  26626  mbfmco  26631  eulerpartlemt  26706  eulerpartlemmf  26710  eulerpart  26717  0rrv  26786  ftc1anclem3  28422  areacirclem5  28441  cytpval  29530  arearect  29544
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