Theorem imaeq2i 5021

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 5019	. 2 |- ( A = B -> ( C " A ) = ( C " B ) )
3	1, 2	ax-mp 5	1 |- ( C " A ) = ( C " B )

Syntax hints:   = wceq 1373   "cima 4679

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 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-3an 983  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-v 2774  df-un 3170  df-in 3172  df-ss 3179  df-sn 3639  df-pr 3640  df-op 3642  df-br 4046  df-opab 4107  df-xp 4682  df-cnv 4684  df-dm 4686  df-rn 4687  df-res 4688  df-ima 4689

This theorem is referenced by:  cnvimarndm  5047  dmco  5192  fnimapr  5641  ssimaex  5642  imauni  5832  isoini2  5890  uniqs  6682  fiintim  7030  fidcenumlemrks  7057  fidcenumlemr  7059  nn0supp  9349  ennnfonelem1  12811  ennnfonelemhf1o  12817  ghmeqker  13640  retopbas  15028