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Theorem nfuni 3849
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 3845 . 2  |-  U. A  =  { y  |  E. z  e.  A  y  e.  z }
2 nfuni.1 . . . 4  |-  F/_ x A
3 nfv 1609 . . . 4  |-  F/ x  y  e.  z
42, 3nfrex 2611 . . 3  |-  F/ x E. z  e.  A  y  e.  z
54nfab 2436 . 2  |-  F/_ x { y  |  E. z  e.  A  y  e.  z }
61, 5nfcxfr 2429 1  |-  F/_ x U. A
Colors of variables: wff set class
Syntax hints:    e. wcel 1696   {cab 2282   F/_wnfc 2419   E.wrex 2557   U.cuni 3843
This theorem is referenced by:  nfiota1  5237  nfrecs  6406  nfsup  7218  ptunimpt  17306  disjabrex  23374  disjabrexf  23375  dfon2lem3  24212  heibor1  26637  stoweidlem28  27880  stoweidlem59  27911  bnj1398  29380  bnj1446  29391  bnj1447  29392  bnj1448  29393  bnj1466  29399  bnj1467  29400  bnj1519  29411  bnj1520  29412  bnj1525  29415  bnj1523  29417
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rex 2562  df-uni 3844
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