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Theorem imaeq2i 5605
Description: Equality theorem for image. (Contributed by NM, 21-Dec-2008.)
Hypothesis
Ref Expression
imaeq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
imaeq2i (𝐶𝐴) = (𝐶𝐵)

Proof of Theorem imaeq2i
StepHypRef Expression
1 imaeq1i.1 . 2 𝐴 = 𝐵
2 imaeq2 5603 . 2 (𝐴 = 𝐵 → (𝐶𝐴) = (𝐶𝐵))
31, 2ax-mp 5 1 (𝐶𝐴) = (𝐶𝐵)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1630  cima 5252
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990  ax-6 2056  ax-7 2092  ax-9 2153  ax-10 2173  ax-11 2189  ax-12 2202  ax-13 2407  ax-ext 2750
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 827  df-3an 1072  df-tru 1633  df-ex 1852  df-nf 1857  df-sb 2049  df-clab 2757  df-cleq 2763  df-clel 2766  df-nfc 2901  df-rab 3069  df-v 3351  df-dif 3724  df-un 3726  df-in 3728  df-ss 3735  df-nul 4062  df-if 4224  df-sn 4315  df-pr 4317  df-op 4321  df-br 4785  df-opab 4845  df-xp 5255  df-cnv 5257  df-dm 5259  df-rn 5260  df-res 5261  df-ima 5262
This theorem is referenced by:  cnvimarndm  5627  dmco  5787  imain  6114  fnimapr  6404  ssimaex  6405  intpreima  6489  resfunexg  6622  imauni  6646  isoini2  6731  frnsuppeq  7457  imacosupp  7486  uniqs  7958  fiint  8392  jech9.3  8840  infxpenlem  9035  hsmexlem4  9452  frnnn0supp  11550  hashkf  13322  ghmeqker  17894  gsumval3lem1  18512  gsumval3lem2  18513  islinds2  20368  lindsind2  20374  snclseqg  22138  retopbas  22783  ismbf3d  23640  i1fima  23664  i1fd  23667  itg1addlem5  23686  limciun  23877  plyeq0  24186  spthispth  26856  0pth  27302  1pthdlem2  27313  eupth2lemb  27414  htth  28109  fcoinver  29750  ffs2  29837  ffsrn  29838  sibfof  30736  eulerpartgbij  30768  eulerpartlemmf  30771  eulerpartlemgh  30774  eulerpart  30778  fiblem  30794  orrvcval4  30860  cvmsss2  31588  opelco3  32008  madeval2  32267  poimirlem3  33738  poimirlem30  33765  mbfposadd  33782  itg2addnclem2  33787  ftc1anclem5  33814  ftc1anclem6  33815  uniqsALTV  34437  pwfi2f1o  38185  brtrclfv2  38538  binomcxp  39075
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