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Theorem nfima 4973
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 4635 . 2  |-  ( A
" B )  =  ran  ( A  |`  B )
2 nfima.1 . . . 4  |-  F/_ x A
3 nfima.2 . . . 4  |-  F/_ x B
42, 3nfres 4904 . . 3  |-  F/_ x
( A  |`  B )
54nfrn 4867 . 2  |-  F/_ x ran  ( A  |`  B )
61, 5nfcxfr 2316 1  |-  F/_ x
( A " B
)
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2306   ran crn 4623    |` cres 4624   "cima 4625
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-rab 2464  df-v 2739  df-un 3133  df-in 3135  df-sn 3597  df-pr 3598  df-op 3600  df-br 4001  df-opab 4062  df-xp 4628  df-cnv 4630  df-dm 4632  df-rn 4633  df-res 4634  df-ima 4635
This theorem is referenced by:  nfimad  4974  csbima12g  4984
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