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Theorem imaeq2i 5010
Description: Equality theorem for image. (Contributed by NM, 21-Dec-2008.)
Hypothesis
Ref Expression
imaeq1i.1  |-  A  =  B
Assertion
Ref Expression
imaeq2i  |-  ( C
" A )  =  ( C " B
)

Proof of Theorem imaeq2i
StepHypRef Expression
1 imaeq1i.1 . 2  |-  A  =  B
2 imaeq2 5008 . 2  |-  ( A  =  B  ->  ( C " A )  =  ( C " B
) )
31, 2ax-mp 8 1  |-  ( C
" A )  =  ( C " B
)
Colors of variables: wff set class
Syntax hints:    = wceq 1623   "cima 4692
This theorem is referenced by:  cnvimarndm  5034  dmco  5181  imain  5328  fnimapr  5583  ssimaex  5584  intpreima  5656  resfunexg  5737  imauni  5772  isoini2  5836  uniqs  6719  fiint  7133  cantnfp1lem1  7380  cantnfp1lem3  7382  oemapso  7384  cantnflem1d  7390  cantnflem1  7391  mapfien  7399  oef1o  7401  cnfcom2lem  7404  jech9.3  7486  infxpenlem  7641  hsmexlem4  8055  nn0supp  10017  hashkf  11339  ghmeqker  14709  gsumval3  15191  snclseqg  17798  retopbas  18269  ismbf3d  19009  i1fima  19033  i1fd  19036  itg1addlem5  19055  limciun  19244  plyeq0  19593  htth  21498  orrvcval4  23665  cvmsss2  23805  domrancur1b  25200  nds  26150  fsuppeq  27259  pwfi2f1o  27260  islinds2  27283  lindsind2  27289
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024  df-opab 4078  df-xp 4695  df-cnv 4697  df-dm 4699  df-rn 4700  df-res 4701  df-ima 4702
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