Theorem imaeq2i 4887

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 4885	. 2 |- ( A = B -> ( C " A ) = ( C " B ) )
3	1, 2	ax-mp 5	1 |- ( C " A ) = ( C " B )

Syntax hints:   = wceq 1332   "cima 4550

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 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122

This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2691  df-un 3080  df-in 3082  df-ss 3089  df-sn 3538  df-pr 3539  df-op 3541  df-br 3938  df-opab 3998  df-xp 4553  df-cnv 4555  df-dm 4557  df-rn 4558  df-res 4559  df-ima 4560

This theorem is referenced by:  cnvimarndm  4911  dmco  5055  fnimapr  5489  ssimaex  5490  imauni  5670  isoini2  5728  uniqs  6495  fiintim  6825  fidcenumlemrks  6849  fidcenumlemr  6851  nn0supp  9053  ennnfonelem1  11956  ennnfonelemhf1o  11962  retopbas  12731