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Theorem imaeq1i 5009
Description: Equality theorem for image. (Contributed by NM, 21-Dec-2008.)
Hypothesis
Ref Expression
imaeq1i.1  |-  A  =  B
Assertion
Ref Expression
imaeq1i  |-  ( A
" C )  =  ( B " C
)

Proof of Theorem imaeq1i
StepHypRef Expression
1 imaeq1i.1 . 2  |-  A  =  B
2 imaeq1 5007 . 2  |-  ( A  =  B  ->  ( A " C )  =  ( B " C
) )
31, 2ax-mp 8 1  |-  ( A
" C )  =  ( B " C
)
Colors of variables: wff set class
Syntax hints:    = wceq 1623   "cima 4692
This theorem is referenced by:  mptpreima  5166  isarep2  5332  suppfif1  7149  marypha2lem4  7191  dfoi  7226  mapfien  7399  r1limg  7443  isf34lem3  8001  compss  8002  fpwwe2lem13  8264  infmsup  9732  gsumval3  15191  gsumzf1o  15196  gsumzaddlem  15203  dprdfid  15252  evlslem2  16249  ssidcn  16985  cnco  16995  qtopres  17389  idqtop  17397  qtopcn  17405  mbfid  18991  mbfres  18999  cncombf  19013  dvlog  19998  efopnlem2  20004  rinvf1o  23038  disjpreima  23361  mbfmcst  23564  mbfmco  23569  0rrv  23654  areacirclem6  24930  domrancur1c  25202  smbkle  26043  nds  26150  funsnfsup  26762  cytpval  27528
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024  df-opab 4078  df-cnv 4697  df-dm 4699  df-rn 4700  df-res 4701  df-ima 4702
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