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Theorem nfco 4444
Description: Bound-variable hypothesis builder for function value. (Contributed by NM, 1-Sep-1999.)
Hypotheses
Ref Expression
nfco.1  F/_
nfco.2  F/_
Assertion
Ref Expression
nfco  F/_  o.

Proof of Theorem nfco
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-co 4297 . 2  o.  { <. , 
>.  |  }
2 nfcv 2175 . . . . . 6  F/_
3 nfco.2 . . . . . 6  F/_
4 nfcv 2175 . . . . . 6  F/_
52, 3, 4nfbr 3799 . . . . 5  F/
6 nfco.1 . . . . . 6  F/_
7 nfcv 2175 . . . . . 6  F/_
84, 6, 7nfbr 3799 . . . . 5  F/
95, 8nfan 1454 . . . 4  F/
109nfex 1525 . . 3  F/
1110nfopab 3816 . 2  F/_ { <. , 
>.  |  }
121, 11nfcxfr 2172 1  F/_  o.
Colors of variables: wff set class
Syntax hints:   wa 97  wex 1378   F/_wnfc 2162   class class class wbr 3755   {copab 3808    o. ccom 4292
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-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-sn 3373  df-pr 3374  df-op 3376  df-br 3756  df-opab 3810  df-co 4297
This theorem is referenced by:  nffun  4867  nftpos  5835
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