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Theorem nfco 4447
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 4300 . 2  o.  { <. , 
>.  |  }
2 nfcv 2178 . . . . . 6  F/_
3 nfco.2 . . . . . 6  F/_
4 nfcv 2178 . . . . . 6  F/_
52, 3, 4nfbr 3802 . . . . 5  F/
6 nfco.1 . . . . . 6  F/_
7 nfcv 2178 . . . . . 6  F/_
84, 6, 7nfbr 3802 . . . . 5  F/
95, 8nfan 1457 . . . 4  F/
109nfex 1528 . . 3  F/
1110nfopab 3819 . 2  F/_ { <. , 
>.  |  }
121, 11nfcxfr 2175 1  F/_  o.
Colors of variables: wff set class
Syntax hints:   wa 97  wex 1381   F/_wnfc 2165   class class class wbr 3758   {copab 3811    o. ccom 4295
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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2556  df-un 2919  df-sn 3376  df-pr 3377  df-op 3379  df-br 3759  df-opab 3813  df-co 4300
This theorem is referenced by:  nffun  4870  nftpos  5839
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