Theorem imaeq2i 5127

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 5125	. 2 |- ( A = B -> ( C " A ) = ( C " B ) )
3	1, 2	ax-mp 5	1 |- ( C " A ) = ( C " B )

This proof depends on syntax axioms:   = wceq 1402   "cima 4779

This proof depends on 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 proof 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 3715  df-pr 3716  df-op 3718  df-br 4132  df-opab 4194  df-xp 4782  df-cnv 4784  df-dm 4786  df-rn 4787  df-res 4788  df-ima 4789

This theorem is used by:  cnvimarndm  5154  dmco  5299  fnimapr  5766  ssimaex  5767  imauni  5970  isoini2  6028  fsuppeq  6491  fsuppeqg  6492  uniqs  6871  fiintim  7242  fidcenumlemrks  7275  fidcenumlemr  7277  fcdmnn0supp  9626  fcdmnn0fsupp  9627  fcdmnn0suppg  9628  nn0supp  9630  ennnfonelem1  13356  ennnfonelemhf1o  13362  ghmeqker  14133  retopbas  15749  eupth2lembfi  16923