Theorem imaeq2i 5119

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 5117	. 2 |- ( A = B -> ( C " A ) = ( C " B ) )
3	1, 2	ax-mp 5	1 |- ( C " A ) = ( C " B )

Syntax hints:   = wceq 1402   "cima 4772

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This theorem depends on definitions:  df-bi 117  df-3an 1011  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-v 2823  df-un 3224  df-in 3226  df-ss 3233  df-sn 3711  df-pr 3712  df-op 3714  df-br 4126  df-opab 4188  df-xp 4775  df-cnv 4777  df-dm 4779  df-rn 4780  df-res 4781  df-ima 4782

This theorem is referenced by:  cnvimarndm  5146  dmco  5291  fnimapr  5757  ssimaex  5758  imauni  5957  isoini2  6015  fsuppeq  6477  fsuppeqg  6478  uniqs  6857  fiintim  7228  fidcenumlemrks  7260  fidcenumlemr  7262  fcdmnn0supp  9594  fcdmnn0fsupp  9595  fcdmnn0suppg  9596  nn0supp  9598  ennnfonelem1  13276  ennnfonelemhf1o  13282  ghmeqker  14051  retopbas  15547  eupth2lembfi  16632