Theorem imaeq2i 5323

Description: Equality theorem for image. (Contributed by NM, 21-Dec-2008.)

Hypothesis

Ref	Expression
imaeq1i.1	|- A = B

Assertion

Ref	Expression
imaeq2i	|- ( C " A ) = ( C " B )

Proof of Theorem imaeq2i

Step	Hyp	Ref	Expression
1		imaeq1i.1	. 2 |- A = B
2		imaeq2 5321	. 2 |- ( A = B -> ( C " A ) = ( C " B ) )
3	1, 2	ax-mp 5	1 |- ( C " A ) = ( C " B )

Syntax hints:   = wceq 1398   "cima 4991

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432

This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 973  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-rab 2813  df-v 3108  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3784  df-if 3930  df-sn 4017  df-pr 4019  df-op 4023  df-br 4440  df-opab 4498  df-xp 4994  df-cnv 4996  df-dm 4998  df-rn 4999  df-res 5000  df-ima 5001

This theorem is referenced by:  cnvimarndm  5346  dmco  5498  imain  5646  fnimapr  5912  ssimaex  5913  intpreima  5994  resfunexg  6112  imauni  6133  isoini2  6210  frnsuppeq  6903  imacosupp  6932  uniqs  7363  fiint  7789  cantnffvalOLD  8073  cantnfp1lem1OLD  8114  cantnfp1lem3OLD  8116  cantnflem1dOLD  8121  cantnflem1OLD  8122  mapfienOLD  8129  oef1oOLD  8133  cnfcom2lemOLD  8144  jech9.3  8223  infxpenlem  8382  hsmexlem4  8800  frnnn0supp  10845  nn0suppOLD  10846  hashkf  12389  ghmeqker  16492  gsumval3OLD  17107  gsumval3lem1  17108  gsumval3lem2  17109  islinds2  19015  lindsind2  19021  snclseqg  20780  retopbas  21433  ismbf3d  22227  i1fima  22251  i1fd  22254  itg1addlem5  22273  limciun  22464  plyeq0  22774  0pth  24774  2pthlem2  24800  constr3pthlem3  24859  htth  26033  fcoinver  27674  ffs2  27782  ffsrn  27783  sibfof  28546  eulerpartgbij  28575  eulerpartlemmf  28578  eulerpartlemgh  28581  eulerpart  28585  fiblem  28601  orrvcval4  28667  cvmsss2  28983  opelco3  29448  mbfposadd  30302  itg2addnclem2  30307  ftc1anclem5  30334  ftc1anclem6  30335  fsuppeq  31282  pwfi2f1o  31283  pwfi2f1oOLD  31284  binomcxp  31503