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Theorem nfco 5173
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 5013 . 2
2 nfcv 2619 . . . . . 6
3 nfco.2 . . . . . 6
4 nfcv 2619 . . . . . 6
52, 3, 4nfbr 4496 . . . . 5
6 nfco.1 . . . . . 6
7 nfcv 2619 . . . . . 6
84, 6, 7nfbr 4496 . . . . 5
95, 8nfan 1928 . . . 4
109nfex 1948 . . 3
1110nfopab 4517 . 2
121, 11nfcxfr 2617 1
Colors of variables: wff setvar class
Syntax hints:  /\wa 369  E.wex 1612  F/_wnfc 2605   class class class wbr 4452  {copab 4509  o.ccom 5008
This theorem is referenced by:  nffun  5615  nftpos  7009  cnmpt11  20164  cnmpt21  20172  cncficcgt0  31691  stoweidlem31  31813  stoweidlem59  31841
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-co 5013
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