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Theorem imaeq2d 4951
Description: Equality theorem for image. (Contributed by FL, 15-Dec-2006.)
Hypothesis
Ref Expression
imaeq1d.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
imaeq2d (𝜑 → (𝐶𝐴) = (𝐶𝐵))

Proof of Theorem imaeq2d
StepHypRef Expression
1 imaeq1d.1 . 2 (𝜑𝐴 = 𝐵)
2 imaeq2 4947 . 2 (𝐴 = 𝐵 → (𝐶𝐴) = (𝐶𝐵))
31, 2syl 14 1 (𝜑 → (𝐶𝐴) = (𝐶𝐵))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1348  cima 4612
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-3an 975  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-un 3125  df-in 3127  df-ss 3134  df-sn 3587  df-pr 3588  df-op 3590  df-br 3988  df-opab 4049  df-xp 4615  df-cnv 4617  df-dm 4619  df-rn 4620  df-res 4621  df-ima 4622
This theorem is referenced by:  imaeq12d  4952  nfimad  4960  elimasng  4977  ressn  5149  foima  5423  f1imacnv  5457  fvco2  5563  fsn2  5667  resfunexg  5714  funfvima3  5726  funiunfvdm  5739  isoselem  5796  fnexALT  6087  eceq1  6544  uniqs2  6569  ecinxp  6584  mapsn  6664  phplem4  6829  phplem4dom  6836  phplem4on  6841  sbthlem2  6931  isbth  6940  resunimafz0  10753  ennnfonelemg  12345  ennnfonelemhf1o  12355  ennnfonelemex  12356  ennnfonelemrn  12361  cnntr  12978  cnptopresti  12991  cnptoprest  12992
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