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Theorem nfco 5030
 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 4879 . 2
2 nfcv 2571 . . . . . 6
3 nfco.2 . . . . . 6
4 nfcv 2571 . . . . . 6
52, 3, 4nfbr 4248 . . . . 5
6 nfco.1 . . . . . 6
7 nfcv 2571 . . . . . 6
84, 6, 7nfbr 4248 . . . . 5
95, 8nfan 1846 . . . 4
109nfex 1865 . . 3
1110nfopab 4265 . 2
121, 11nfcxfr 2568 1
 Colors of variables: wff set class Syntax hints:   wa 359  wex 1550  wnfc 2558   class class class wbr 4204  copab 4257   ccom 4874 This theorem is referenced by:  nffun  5468  nftpos  6506  cnmpt11  17687  cnmpt21  17695  stoweidlem31  27747  stoweidlem59  27775 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-br 4205  df-opab 4259  df-co 4879
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