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Theorem imaeq1i 5200
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 5198 . 2  |-  ( A  =  B  ->  ( A " C )  =  ( B " C
) )
31, 2ax-mp 8 1  |-  ( A
" C )  =  ( B " C
)
Colors of variables: wff set class
Syntax hints:    = wceq 1652   "cima 4881
This theorem is referenced by:  mptpreima  5363  isarep2  5533  suppfif1  7400  marypha2lem4  7443  dfoi  7480  mapfien  7653  r1limg  7697  isf34lem3  8255  compss  8256  fpwwe2lem13  8517  infmsup  9986  gsumval3  15514  gsumzf1o  15519  gsumzaddlem  15526  dprdfid  15575  evlslem2  16568  ssidcn  17319  cnco  17330  qtopres  17730  idqtop  17738  qtopcn  17746  mbfid  19528  mbfres  19536  cncombf  19550  dvlog  20542  efopnlem2  20548  disjpreima  24026  imadifxp  24038  rinvf1o  24042  mbfmcst  24609  mbfmco  24614  sitmcl  24663  0rrv  24709  ftc1anclem3  26282  areacirclem5  26296  funsnfsup  26743  cytpval  27505
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-3an 938  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-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213  df-opab 4267  df-cnv 4886  df-dm 4888  df-rn 4889  df-res 4890  df-ima 4891
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