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Theorem nfun 3093
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  F/_
nfun.2  F/_
Assertion
Ref Expression
nfun  F/_  u.

Proof of Theorem nfun
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-un 2916 . 2  u.  {  |  }
2 nfun.1 . . . . 5  F/_
32nfcri 2169 . . . 4  F/
4 nfun.2 . . . . 5  F/_
54nfcri 2169 . . . 4  F/
63, 5nfor 1463 . . 3  F/
76nfab 2179 . 2  F/_ {  |  }
81, 7nfcxfr 2172 1  F/_  u.
Colors of variables: wff set class
Syntax hints:   wo 628   wcel 1390   {cab 2023   F/_wnfc 2162    u. cun 2909
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-un 2916
This theorem is referenced by:  nfsuc  4111
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