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Theorem imaeq2d 4971
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 4967 . 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 4630
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 2740  df-un 3134  df-in 3136  df-ss 3143  df-sn 3599  df-pr 3600  df-op 3602  df-br 4005  df-opab 4066  df-xp 4633  df-cnv 4635  df-dm 4637  df-rn 4638  df-res 4639  df-ima 4640
This theorem is referenced by:  imaeq12d  4972  nfimad  4980  elimasng  4997  ressn  5170  foima  5444  f1imacnv  5479  fvco2  5586  fsn2  5691  resfunexg  5738  funfvima3  5751  funiunfvdm  5764  isoselem  5821  fnexALT  6112  eceq1  6570  uniqs2  6595  ecinxp  6610  mapsn  6690  phplem4  6855  phplem4dom  6862  phplem4on  6867  sbthlem2  6957  isbth  6966  resunimafz0  10811  ennnfonelemg  12404  ennnfonelemhf1o  12414  ennnfonelemex  12415  ennnfonelemrn  12420  cnntr  13728  cnptopresti  13741  cnptoprest  13742
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