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Theorem imaeq2i 5202
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 5200 . 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 1653   "cima 4882
This theorem is referenced by:  cnvimarndm  5226  dmco  5379  imain  5530  fnimapr  5788  ssimaex  5789  intpreima  5862  resfunexg  5958  imauni  5994  isoini2  6060  uniqs  6965  fiint  7384  cantnfp1lem1  7635  cantnfp1lem3  7637  oemapso  7639  cantnflem1d  7645  cantnflem1  7646  mapfien  7654  oef1o  7656  cnfcom2lem  7659  jech9.3  7741  infxpenlem  7896  hsmexlem4  8310  nn0supp  10274  hashkf  11621  ghmeqker  15033  gsumval3  15515  snclseqg  18146  retopbas  18795  ismbf3d  19547  i1fima  19571  i1fd  19574  itg1addlem5  19593  limciun  19782  plyeq0  20131  0pth  21571  2pthlem2  21597  constr3pthlem3  21645  htth  22422  sibfof  24655  orrvcval4  24723  cvmsss2  24962  opelco3  25404  mbfposadd  26255  itg2addnclem2  26258  ftc1anclem5  26285  ftc1anclem6  26286  fsuppeq  27237  pwfi2f1o  27238  islinds2  27261  lindsind2  27267
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-rab 2715  df-v 2959  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-nul 3630  df-if 3741  df-sn 3821  df-pr 3822  df-op 3824  df-br 4214  df-opab 4268  df-xp 4885  df-cnv 4887  df-dm 4889  df-rn 4890  df-res 4891  df-ima 4892
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