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Theorem nfco 4699
 Description: Bound-variable hypothesis builder for function value. (Contributed by NM, 1-Sep-1999.)
Hypotheses
Ref Expression
nfco.1
nfco.2
Assertion
Ref Expression
nfco

Proof of Theorem nfco
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-co 4543 . 2
2 nfcv 2279 . . . . . 6
3 nfco.2 . . . . . 6
4 nfcv 2279 . . . . . 6
52, 3, 4nfbr 3969 . . . . 5
6 nfco.1 . . . . . 6
7 nfcv 2279 . . . . . 6
84, 6, 7nfbr 3969 . . . . 5
95, 8nfan 1544 . . . 4
109nfex 1616 . . 3
1110nfopab 3991 . 2
121, 11nfcxfr 2276 1
 Colors of variables: wff set class Syntax hints:   wa 103  wex 1468  wnfc 2266   class class class wbr 3924  copab 3983   ccom 4538 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-un 3070  df-sn 3528  df-pr 3529  df-op 3531  df-br 3925  df-opab 3985  df-co 4543 This theorem is referenced by:  nffun  5141  nftpos  6169  cnmpt11  12441  cnmpt21  12449
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