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Theorem imaeq1i 5332
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 5330 . 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 1379   "cima 5002
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-rab 2823  df-v 3115  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034  df-br 4448  df-opab 4506  df-cnv 5007  df-dm 5009  df-rn 5010  df-res 5011  df-ima 5012
This theorem is referenced by:  mptpreima  5498  isarep2  5666  suppun  6917  supp0cosupp0  6936  imacosupp  6937  fsuppun  7844  fsuppcolem  7856  marypha2lem4  7894  dfoi  7932  mapfienOLD  8134  r1limg  8185  isf34lem3  8751  compss  8752  fpwwe2lem13  9016  infmsup  10517  gsumval3OLD  16699  gsumzf1o  16708  gsumzf1oOLD  16711  gsumzaddlemOLD  16727  dprdfidOLD  16854  funsnfsupOLD  18027  ssidcn  19522  cnco  19533  qtopres  19934  idqtop  19942  qtopcn  19950  mbfid  21778  mbfres  21786  cncombf  21800  dvlog  22760  efopnlem2  22766  disjpreima  27118  imadifxp  27131  rinvf1o  27145  mbfmcst  27870  mbfmco  27875  eulerpartlemt  27950  eulerpartlemmf  27954  eulerpart  27961  0rrv  28030  ftc1anclem3  29669  areacirclem5  29688  cytpval  30774  arearect  30788  0cnf  31215  mbf0  31275  fourierdlem62  31469
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