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Theorem nfima 5196
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 4867 . 2  |-  ( A
" B )  =  ran  ( A  |`  B )
2 nfima.1 . . . 4  |-  F/_ x A
3 nfima.2 . . . 4  |-  F/_ x B
42, 3nfres 5127 . . 3  |-  F/_ x
( A  |`  B )
54nfrn 5097 . 2  |-  F/_ x ran  ( A  |`  B )
61, 5nfcxfr 2589 1  |-  F/_ x
( A " B
)
Colors of variables: wff setvar class
Syntax hints:   F/_wnfc 2577   ran crn 4855    |` cres 4856   "cima 4857
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-rab 2791  df-v 3089  df-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3768  df-if 3916  df-sn 4003  df-pr 4005  df-op 4009  df-br 4427  df-opab 4485  df-xp 4860  df-cnv 4862  df-dm 4864  df-rn 4865  df-res 4866  df-ima 4867
This theorem is referenced by:  nfimad  5197  csbima12  5205  csbima12gOLD  5206  nfpred  5404  nfsup  7971  nfoi  8029  nfseq  12220  gsum2d2  17541  ptbasfi  20527  mbfposr  22485  itg1climres  22549  limciun  22726  funimass4f  28074  poimirlem16  31660  poimirlem19  31663  aomclem8  35625  areaquad  35800  binomcxplemdvbinom  36339  binomcxplemdvsum  36341  binomcxplemnotnn0  36342  rfcnpre1  36980  rfcnpre2  36992
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