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Theorem nfin 3207
 Description: Bound-variable hypothesis builder for the intersection of classes. (Contributed by NM, 15-Sep-2003.) (Revised by Mario Carneiro, 14-Oct-2016.)
Hypotheses
Ref Expression
nfin.1
nfin.2
Assertion
Ref Expression
nfin

Proof of Theorem nfin
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfin5 3007 . 2
2 nfin.2 . . . 4
32nfcri 2223 . . 3
4 nfin.1 . . 3
53, 4nfrabxy 2548 . 2
61, 5nfcxfr 2226 1
 Colors of variables: wff set class Syntax hints:   wcel 1439  wnfc 2216  crab 2364   cin 2999 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071 This theorem depends on definitions:  df-bi 116  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-rab 2369  df-in 3006 This theorem is referenced by:  csbing  3208  nfres  4728
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