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Theorem nfuni 3833
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  |-  F/_ x A
Assertion
Ref Expression
nfuni  |-  F/_ x U. A

Proof of Theorem nfuni
Dummy variables  y 
z are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 dfuni2 3829 . 2  |-  U. A  =  { y  |  E. z  e.  A  y  e.  z }
2 nfuni.1 . . . 4  |-  F/_ x A
3 nfv 1605 . . . 4  |-  F/ x  y  e.  z
42, 3nfrex 2598 . . 3  |-  F/ x E. z  e.  A  y  e.  z
54nfab 2423 . 2  |-  F/_ x { y  |  E. z  e.  A  y  e.  z }
61, 5nfcxfr 2416 1  |-  F/_ x U. A
Colors of variables: wff set class
Syntax hints:    e. wcel 1684   {cab 2269   F/_wnfc 2406   E.wrex 2544   U.cuni 3827
This theorem is referenced by:  nfiota1  5221  nfrecs  6390  nfsup  7202  ptunimpt  17290  disjabrex  23359  disjabrexf  23360  dfon2lem3  24141  heibor1  26534  stoweidlem28  27777  stoweidlem59  27808  bnj1398  29064  bnj1446  29075  bnj1447  29076  bnj1448  29077  bnj1466  29083  bnj1467  29084  bnj1519  29095  bnj1520  29096  bnj1525  29099  bnj1523  29101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-rex 2549  df-uni 3828
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