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Theorem nfima 5020
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 4702 . 2  |-  ( A
" B )  =  ran  ( A  |`  B )
2 nfima.1 . . . 4  |-  F/_ x A
3 nfima.2 . . . 4  |-  F/_ x B
42, 3nfres 4957 . . 3  |-  F/_ x
( A  |`  B )
54nfrn 4921 . 2  |-  F/_ x ran  ( A  |`  B )
61, 5nfcxfr 2416 1  |-  F/_ x
( A " B
)
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2406   ran crn 4690    |` cres 4691   "cima 4692
This theorem is referenced by:  nfimad  5021  csbima12g  5022  nfsup  7202  nfoi  7229  nfseq  11056  gsum2d2  15225  ptbasfi  17276  mbfposr  19007  itg1climres  19069  limciun  19244  funimass4f  23042  aomclem8  27159  rfcnpre1  27690  rfcnpre2  27702
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024  df-opab 4078  df-xp 4695  df-cnv 4697  df-dm 4699  df-rn 4700  df-res 4701  df-ima 4702
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