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Theorem imaeq1i 6075
Description: Equality theorem for image. (Contributed by NM, 21-Dec-2008.)
Hypothesis
Ref Expression
imaeq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
imaeq1i (𝐴𝐶) = (𝐵𝐶)

Proof of Theorem imaeq1i
StepHypRef Expression
1 imaeq1i.1 . 2 𝐴 = 𝐵
2 imaeq1 6073 . 2 (𝐴 = 𝐵 → (𝐴𝐶) = (𝐵𝐶))
31, 2ax-mp 5 1 (𝐴𝐶) = (𝐵𝐶)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1540  cima 5688
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-rab 3437  df-v 3482  df-dif 3954  df-un 3956  df-in 3958  df-ss 3968  df-nul 4334  df-if 4526  df-sn 4627  df-pr 4629  df-op 4633  df-br 5144  df-opab 5206  df-cnv 5693  df-dm 5695  df-rn 5696  df-res 5697  df-ima 5698
This theorem is referenced by:  mptpreima  6258  csbpredg  6327  isarep2  6658  suppun  8209  suppco  8231  fsuppun  9427  fsuppcolem  9441  marypha2lem4  9478  dfoi  9551  r1limg  9811  isf34lem3  10415  compss  10416  fpwwe2lem12  10682  infrenegsup  12251  gsumzf1o  19930  ssidcn  23263  cnco  23274  qtopres  23706  idqtop  23714  qtopcn  23722  mbfid  25670  mbfres  25679  cncombf  25693  dvlog  26693  efopnlem2  26699  seqsval  28294  seqsfn  28315  seqsp1  28317  eucrct2eupth  30264  disjpreima  32597  imadifxp  32614  rinvf1o  32640  suppun2  32693  cyc3genpm  33172  elrgspnsubrunlem2  33252  isconstr  33777  mbfmcst  34261  mbfmco  34266  sitmcl  34353  eulerpartlemt  34373  eulerpartlemmf  34377  eulerpart  34384  0rrv  34453  mclsppslem  35588  bj-iminvid  37196  mptsnun  37340  poimirlem3  37630  ftc1anclem3  37702  areacirclem5  37719  cytpval  43214  arearect  43227  brtrclfv2  43740  0cnf  45892  fourierdlem62  46183  smfco  46817
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