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Theorem nfima 4769
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 4441 . 2 (𝐴𝐵) = ran (𝐴𝐵)
2 nfima.1 . . . 4 𝑥𝐴
3 nfima.2 . . . 4 𝑥𝐵
42, 3nfres 4703 . . 3 𝑥(𝐴𝐵)
54nfrn 4668 . 2 𝑥ran (𝐴𝐵)
61, 5nfcxfr 2225 1 𝑥(𝐴𝐵)
Colors of variables: wff set class
Syntax hints:  wnfc 2215  ran crn 4429  cres 4430  cima 4431
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-3an 926  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-rab 2368  df-v 2621  df-un 3001  df-in 3003  df-sn 3447  df-pr 3448  df-op 3450  df-br 3838  df-opab 3892  df-xp 4434  df-cnv 4436  df-dm 4438  df-rn 4439  df-res 4440  df-ima 4441
This theorem is referenced by:  nfimad  4770  csbima12g  4780
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