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Theorem imaeq2i 5026
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 5024 . 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 1632   "cima 4708
This theorem is referenced by:  cnvimarndm  5050  dmco  5197  imain  5344  fnimapr  5599  ssimaex  5600  intpreima  5672  resfunexg  5753  imauni  5788  isoini2  5852  uniqs  6735  fiint  7149  cantnfp1lem1  7396  cantnfp1lem3  7398  oemapso  7400  cantnflem1d  7406  cantnflem1  7407  mapfien  7415  oef1o  7417  cnfcom2lem  7420  jech9.3  7502  infxpenlem  7657  hsmexlem4  8071  nn0supp  10033  hashkf  11355  ghmeqker  14725  gsumval3  15207  snclseqg  17814  retopbas  18285  ismbf3d  19025  i1fima  19049  i1fd  19052  itg1addlem5  19071  limciun  19260  plyeq0  19609  htth  21514  orrvcval4  23680  cvmsss2  23820  itg2addnclem2  25004  domrancur1b  25303  nds  26253  fsuppeq  27362  pwfi2f1o  27363  islinds2  27386  lindsind2  27392  0pth  28356  constr3pthlem3  28403
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-br 4040  df-opab 4094  df-xp 4711  df-cnv 4713  df-dm 4715  df-rn 4716  df-res 4717  df-ima 4718
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