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Theorem nfun 3659
 Description: Bound-variable hypothesis builder for the union of classes. (Contributed by NM, 15-Sep-2003.) (Revised by Mario Carneiro, 14-Oct-2016.)
Hypotheses
Ref Expression
nfun.1
nfun.2
Assertion
Ref Expression
nfun

Proof of Theorem nfun
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-un 3480 . 2
2 nfun.1 . . . . 5
32nfcri 2612 . . . 4
4 nfun.2 . . . . 5
54nfcri 2612 . . . 4
63, 5nfor 1935 . . 3
76nfab 2623 . 2
81, 7nfcxfr 2617 1
 Colors of variables: wff setvar class Syntax hints:  \/wo 368  e.wcel 1818  {cab 2442  F/_wnfc 2605  u.cun 3473 This theorem is referenced by:  csbun  3857  csbungOLD  3858  nfsuc  4954  nfsup  7931  iuncon  19929  ordtconlem1  27906  esumsplit  28063  measvuni  28185  nfsymdif  29472  bnj958  33998  bnj1000  33999  bnj1408  34092  bnj1446  34101  bnj1447  34102  bnj1448  34103  bnj1466  34109  bnj1467  34110 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-un 3480
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