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Theorem imaeq2d 4970
Description: Equality theorem for image. (Contributed by FL, 15-Dec-2006.)
Hypothesis
Ref Expression
imaeq1d.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
imaeq2d  |-  ( ph  ->  ( C " A
)  =  ( C
" B ) )

Proof of Theorem imaeq2d
StepHypRef Expression
1 imaeq1d.1 . 2  |-  ( ph  ->  A  =  B )
2 imaeq2 4966 . 2  |-  ( A  =  B  ->  ( C " A )  =  ( C " B
) )
31, 2syl 14 1  |-  ( ph  ->  ( C " A
)  =  ( C
" B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1353   "cima 4629
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-un 3133  df-in 3135  df-ss 3142  df-sn 3598  df-pr 3599  df-op 3601  df-br 4004  df-opab 4065  df-xp 4632  df-cnv 4634  df-dm 4636  df-rn 4637  df-res 4638  df-ima 4639
This theorem is referenced by:  imaeq12d  4971  nfimad  4979  elimasng  4996  ressn  5169  foima  5443  f1imacnv  5478  fvco2  5585  fsn2  5690  resfunexg  5737  funfvima3  5750  funiunfvdm  5763  isoselem  5820  fnexALT  6111  eceq1  6569  uniqs2  6594  ecinxp  6609  mapsn  6689  phplem4  6854  phplem4dom  6861  phplem4on  6866  sbthlem2  6956  isbth  6965  resunimafz0  10806  ennnfonelemg  12398  ennnfonelemhf1o  12408  ennnfonelemex  12409  ennnfonelemrn  12414  cnntr  13618  cnptopresti  13631  cnptoprest  13632
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