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Theorem imaeq1d 4742
Description: Equality theorem for image. (Contributed by FL, 15-Dec-2006.)
Hypothesis
Ref Expression
imaeq1d.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
imaeq1d  |-  ( ph  ->  ( A " C
)  =  ( B
" C ) )

Proof of Theorem imaeq1d
StepHypRef Expression
1 imaeq1d.1 . 2  |-  ( ph  ->  A  =  B )
2 imaeq1 4738 . 2  |-  ( A  =  B  ->  ( A " C )  =  ( B " C
) )
31, 2syl 14 1  |-  ( ph  ->  ( A " C
)  =  ( B
" C ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1287   "cima 4416
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-3an 924  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-v 2617  df-un 2992  df-in 2994  df-ss 3001  df-sn 3437  df-pr 3438  df-op 3440  df-br 3823  df-opab 3877  df-cnv 4421  df-dm 4423  df-rn 4424  df-res 4425  df-ima 4426
This theorem is referenced by:  imaeq12d  4744  nfimad  4752  f1imacnv  5235  foimacnv  5236  suppssof1  5831  ssenen  6521
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