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Theorem imaeq2i 4696
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
StepHypRef Expression
1 imaeq1i.1 . 2  |-  A  =  B
2 imaeq2 4694 . 2  |-  ( A  =  B  ->  ( C " A )  =  ( C " B
) )
31, 2ax-mp 7 1  |-  ( C
" A )  =  ( C " B
)
Colors of variables: wff set class
Syntax hints:    = wceq 1285   "cima 4374
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-sn 3412  df-pr 3413  df-op 3415  df-br 3794  df-opab 3848  df-xp 4377  df-cnv 4379  df-dm 4381  df-rn 4382  df-res 4383  df-ima 4384
This theorem is referenced by:  cnvimarndm  4719  dmco  4859  fnimapr  5265  ssimaex  5266  imauni  5432  isoini2  5489  uniqs  6230  nn0supp  8407
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