Theorem imaeq1i 5065

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 5063	. 2 |- ( A = B -> ( A " C ) = ( B " C ) )
3	1, 2	ax-mp 5	1 |- ( A " C ) = ( B " C )

Syntax hints:   = wceq 1395   "cima 4722

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-3an 1004  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-v 2801  df-un 3201  df-in 3203  df-ss 3210  df-sn 3672  df-pr 3673  df-op 3675  df-br 4084  df-opab 4146  df-cnv 4727  df-dm 4729  df-rn 4730  df-res 4731  df-ima 4732

This theorem is referenced by:  mptpreima  5222  isarep2  5408  infrenegsupex  9789  infxrnegsupex  11774  ssidcn  14884  cnco  14895