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Theorem nfima 5214
Description: Bound-variable hypothesis builder for image. (Contributed by NM, 30-Dec-1996.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)
Hypotheses
Ref Expression
nfima.1  |-  F/_ x A
nfima.2  |-  F/_ x B
Assertion
Ref Expression
nfima  |-  F/_ x
( A " B
)

Proof of Theorem nfima
StepHypRef Expression
1 df-ima 4894 . 2  |-  ( A
" B )  =  ran  ( A  |`  B )
2 nfima.1 . . . 4  |-  F/_ x A
3 nfima.2 . . . 4  |-  F/_ x B
42, 3nfres 5151 . . 3  |-  F/_ x
( A  |`  B )
54nfrn 5115 . 2  |-  F/_ x ran  ( A  |`  B )
61, 5nfcxfr 2571 1  |-  F/_ x
( A " B
)
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2561   ran crn 4882    |` cres 4883   "cima 4884
This theorem is referenced by:  nfimad  5215  csbima12g  5216  nfsup  7459  nfoi  7486  nfseq  11338  gsum2d2  15553  ptbasfi  17618  mbfposr  19547  itg1climres  19609  limciun  19786  funimass4f  24049  nfpred  25449  aomclem8  27150  rfcnpre1  27680  rfcnpre2  27692
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4216  df-opab 4270  df-xp 4887  df-cnv 4889  df-dm 4891  df-rn 4892  df-res 4893  df-ima 4894
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