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Theorem nfima 4898
 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 𝑥𝐴
nfima.2 𝑥𝐵
Assertion
Ref Expression
nfima 𝑥(𝐴𝐵)

Proof of Theorem nfima
StepHypRef Expression
1 df-ima 4561 . 2 (𝐴𝐵) = ran (𝐴𝐵)
2 nfima.1 . . . 4 𝑥𝐴
3 nfima.2 . . . 4 𝑥𝐵
42, 3nfres 4830 . . 3 𝑥(𝐴𝐵)
54nfrn 4793 . 2 𝑥ran (𝐴𝐵)
61, 5nfcxfr 2279 1 𝑥(𝐴𝐵)
 Colors of variables: wff set class Syntax hints:  Ⅎwnfc 2269  ran crn 4549   ↾ cres 4550   “ cima 4551 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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-rab 2426  df-v 2692  df-un 3081  df-in 3083  df-sn 3539  df-pr 3540  df-op 3542  df-br 3939  df-opab 3999  df-xp 4554  df-cnv 4556  df-dm 4558  df-rn 4559  df-res 4560  df-ima 4561 This theorem is referenced by:  nfimad  4899  csbima12g  4909
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