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Theorem nfima 4857
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 4520 . 2  |-  ( A
" B )  =  ran  ( A  |`  B )
2 nfima.1 . . . 4  |-  F/_ x A
3 nfima.2 . . . 4  |-  F/_ x B
42, 3nfres 4789 . . 3  |-  F/_ x
( A  |`  B )
54nfrn 4752 . 2  |-  F/_ x ran  ( A  |`  B )
61, 5nfcxfr 2253 1  |-  F/_ x
( A " B
)
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2243   ran crn 4508    |` cres 4509   "cima 4510
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-3an 947  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-rab 2400  df-v 2660  df-un 3043  df-in 3045  df-sn 3501  df-pr 3502  df-op 3504  df-br 3898  df-opab 3958  df-xp 4513  df-cnv 4515  df-dm 4517  df-rn 4518  df-res 4519  df-ima 4520
This theorem is referenced by:  nfimad  4858  csbima12g  4868
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