Theorem imaeq1i 4967

Description: Equality theorem for image. (Contributed by NM, 21-Dec-2008.)

Hypothesis

Ref	Expression
imaeq1i.1	|- A = B

Assertion

Ref	Expression
imaeq1i	|- ( A " C ) = ( B " C )

Proof of Theorem imaeq1i

Step	Hyp	Ref	Expression
1		imaeq1i.1	. 2 |- A = B
2		imaeq1 4965	. 2 |- ( A = B -> ( A " C ) = ( B " C ) )
3	1, 2	ax-mp 5	1 |- ( A " C ) = ( B " C )

Syntax hints:   = wceq 1353   "cima 4629

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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-un 3133  df-in 3135  df-ss 3142  df-sn 3598  df-pr 3599  df-op 3601  df-br 4004  df-opab 4065  df-cnv 4634  df-dm 4636  df-rn 4637  df-res 4638  df-ima 4639

This theorem is referenced by:  mptpreima  5122  isarep2  5303  infrenegsupex  9592  infxrnegsupex  11266  ssidcn  13603  cnco  13614