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Theorem imaeq1i 5705
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 5703 . 2 (𝐴 = 𝐵 → (𝐴𝐶) = (𝐵𝐶))
31, 2ax-mp 5 1 (𝐴𝐶) = (𝐵𝐶)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1658  cima 5346
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-9 2175  ax-10 2194  ax-11 2209  ax-12 2222  ax-13 2391  ax-ext 2804
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 881  df-3an 1115  df-tru 1662  df-ex 1881  df-nf 1885  df-sb 2070  df-clab 2813  df-cleq 2819  df-clel 2822  df-nfc 2959  df-rab 3127  df-v 3417  df-dif 3802  df-un 3804  df-in 3806  df-ss 3813  df-nul 4146  df-if 4308  df-sn 4399  df-pr 4401  df-op 4405  df-br 4875  df-opab 4937  df-cnv 5351  df-dm 5353  df-rn 5354  df-res 5355  df-ima 5356
This theorem is referenced by:  mptpreima  5870  isarep2  6212  suppun  7580  supp0cosupp0  7600  imacosupp  7601  fsuppun  8564  fsuppcolem  8576  marypha2lem4  8614  dfoi  8686  r1limg  8912  isf34lem3  9513  compss  9514  fpwwe2lem13  9780  infrenegsup  11337  gsumzf1o  18667  ssidcn  21431  cnco  21442  qtopres  21873  idqtop  21881  qtopcn  21889  mbfid  23802  mbfres  23811  cncombf  23825  dvlog  24797  efopnlem2  24803  eucrct2eupthOLD  27624  eucrct2eupth  27625  disjpreima  29945  imadifxp  29962  rinvf1o  29982  mbfmcst  30867  mbfmco  30872  sitmcl  30959  eulerpartlemt  30979  eulerpartlemmf  30983  eulerpart  30990  0rrv  31060  mclsppslem  32027  csbpredg  33719  mptsnun  33733  poimirlem3  33957  ftc1anclem3  34031  areacirclem5  34048  cytpval  38631  arearect  38644  brtrclfv2  38861  0cnf  40886  fourierdlem62  41180  smfco  41804
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