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Theorem imaeq1i 5322
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 5320 . 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 1398   "cima 4991
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 973  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-rab 2813  df-v 3108  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3784  df-if 3930  df-sn 4017  df-pr 4019  df-op 4023  df-br 4440  df-opab 4498  df-cnv 4996  df-dm 4998  df-rn 4999  df-res 5000  df-ima 5001
This theorem is referenced by:  mptpreima  5483  isarep2  5650  suppun  6912  supp0cosupp0  6931  imacosupp  6932  fsuppun  7840  fsuppcolem  7852  marypha2lem4  7890  dfoi  7928  mapfienOLD  8129  r1limg  8180  isf34lem3  8746  compss  8747  fpwwe2lem13  9009  infmsup  10516  gsumval3OLD  17110  gsumzf1o  17119  gsumzf1oOLD  17122  gsumzaddlemOLD  17138  dprdfidOLD  17262  funsnfsupOLD  18454  ssidcn  19926  cnco  19937  qtopres  20368  idqtop  20376  qtopcn  20384  mbfid  22212  mbfres  22220  cncombf  22234  dvlog  23203  efopnlem2  23209  disjpreima  27658  imadifxp  27675  rinvf1o  27694  mbfmcst  28470  mbfmco  28475  eulerpartlemt  28577  eulerpartlemmf  28581  eulerpart  28588  0rrv  28657  mclsppslem  29210  ftc1anclem3  30335  areacirclem5  30354  cytpval  31413  arearect  31427  0cnf  31921  mbf0  31998  fourierdlem62  32193  brtrclfv2  38261
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