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Theorem imaeq1i 5451
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 5449 . 2 (𝐴 = 𝐵 → (𝐴𝐶) = (𝐵𝐶))
31, 2ax-mp 5 1 (𝐴𝐶) = (𝐵𝐶)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1481  cima 5107
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-9 1997  ax-10 2017  ax-11 2032  ax-12 2045  ax-13 2244  ax-ext 2600
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1038  df-tru 1484  df-ex 1703  df-nf 1708  df-sb 1879  df-clab 2607  df-cleq 2613  df-clel 2616  df-nfc 2751  df-rab 2918  df-v 3197  df-dif 3570  df-un 3572  df-in 3574  df-ss 3581  df-nul 3908  df-if 4078  df-sn 4169  df-pr 4171  df-op 4175  df-br 4645  df-opab 4704  df-cnv 5112  df-dm 5114  df-rn 5115  df-res 5116  df-ima 5117
This theorem is referenced by:  mptpreima  5616  isarep2  5966  suppun  7300  supp0cosupp0  7319  imacosupp  7320  fsuppun  8279  fsuppcolem  8291  marypha2lem4  8329  dfoi  8401  r1limg  8619  isf34lem3  9182  compss  9183  fpwwe2lem13  9449  infrenegsup  10991  gsumzf1o  18294  ssidcn  21040  cnco  21051  qtopres  21482  idqtop  21490  qtopcn  21498  mbfid  23384  mbfres  23392  cncombf  23406  dvlog  24378  efopnlem2  24384  eucrct2eupth  27085  disjpreima  29369  imadifxp  29386  rinvf1o  29405  mbfmcst  30295  mbfmco  30300  sitmcl  30387  eulerpartlemt  30407  eulerpartlemmf  30411  eulerpart  30418  0rrv  30487  mclsppslem  31454  csbpredg  33143  mptsnun  33157  poimirlem3  33383  ftc1anclem3  33458  areacirclem5  33475  cytpval  37606  arearect  37620  brtrclfv2  37838  0cnf  39853  mbf0  39936  fourierdlem62  40148  smfco  40772
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