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Theorem imaeq2i 4939
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 4937 . 2  |-  ( A  =  B  ->  ( C " A )  =  ( C " B
) )
31, 2ax-mp 5 1  |-  ( C
" A )  =  ( C " B
)
Colors of variables: wff set class
Syntax hints:    = wceq 1342   "cima 4602
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1434  ax-7 1435  ax-gen 1436  ax-ie1 1480  ax-ie2 1481  ax-8 1491  ax-10 1492  ax-11 1493  ax-i12 1494  ax-bndl 1496  ax-4 1497  ax-17 1513  ax-i9 1517  ax-ial 1521  ax-i5r 1522  ax-ext 2146
This theorem depends on definitions:  df-bi 116  df-3an 969  df-tru 1345  df-nf 1448  df-sb 1750  df-clab 2151  df-cleq 2157  df-clel 2160  df-nfc 2295  df-v 2724  df-un 3116  df-in 3118  df-ss 3125  df-sn 3577  df-pr 3578  df-op 3580  df-br 3978  df-opab 4039  df-xp 4605  df-cnv 4607  df-dm 4609  df-rn 4610  df-res 4611  df-ima 4612
This theorem is referenced by:  cnvimarndm  4963  dmco  5107  fnimapr  5541  ssimaex  5542  imauni  5724  isoini2  5782  uniqs  6551  fiintim  6886  fidcenumlemrks  6910  fidcenumlemr  6912  nn0supp  9158  ennnfonelem1  12303  ennnfonelemhf1o  12309  retopbas  13090
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