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Theorem nfima 5178
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 4858 . 2  |-  ( A
" B )  =  ran  ( A  |`  B )
2 nfima.1 . . . 4  |-  F/_ x A
3 nfima.2 . . . 4  |-  F/_ x B
42, 3nfres 5115 . . 3  |-  F/_ x
( A  |`  B )
54nfrn 5079 . 2  |-  F/_ x ran  ( A  |`  B )
61, 5nfcxfr 2545 1  |-  F/_ x
( A " B
)
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2535   ran crn 4846    |` cres 4847   "cima 4848
This theorem is referenced by:  nfimad  5179  csbima12g  5180  nfsup  7420  nfoi  7447  nfseq  11296  gsum2d2  15511  ptbasfi  17574  mbfposr  19505  itg1climres  19567  limciun  19742  funimass4f  24005  aomclem8  27035  rfcnpre1  27565  rfcnpre2  27577
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-rab 2683  df-v 2926  df-dif 3291  df-un 3293  df-in 3295  df-ss 3302  df-nul 3597  df-if 3708  df-sn 3788  df-pr 3789  df-op 3791  df-br 4181  df-opab 4235  df-xp 4851  df-cnv 4853  df-dm 4855  df-rn 4856  df-res 4857  df-ima 4858
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