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Theorem nfuni 3745
 Description: Bound-variable hypothesis builder for union. (Contributed by NM, 30-Dec-1996.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)
Hypothesis
Ref Expression
nfuni.1
Assertion
Ref Expression
nfuni

Proof of Theorem nfuni
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 dfuni2 3741 . 2
2 nfuni.1 . . . 4
3 nfv 1508 . . . 4
42, 3nfrexxy 2472 . . 3
54nfab 2286 . 2
61, 5nfcxfr 2278 1
 Colors of variables: wff set class Syntax hints:  cab 2125  wnfc 2268  wrex 2417  cuni 3739 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-rex 2422  df-uni 3740 This theorem is referenced by:  nfiota1  5093  nfrecs  6207  nfsup  6882
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