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Theorem nfdc 1639
 Description: If is not free in , it is not free in DECID . (Contributed by Jim Kingdon, 11-Mar-2018.)
Hypothesis
Ref Expression
nfdc.1
Assertion
Ref Expression
nfdc DECID

Proof of Theorem nfdc
StepHypRef Expression
1 df-dc 821 . 2 DECID
2 nfdc.1 . . 3
32nfn 1638 . . 3
42, 3nfor 1554 . 2
51, 4nfxfr 1454 1 DECID
 Colors of variables: wff set class Syntax hints:   wn 3   wo 698  DECID wdc 820  wnf 1440 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-in1 604  ax-in2 605  ax-io 699  ax-5 1427  ax-gen 1429  ax-ie2 1474  ax-4 1490  ax-ial 1514 This theorem depends on definitions:  df-bi 116  df-dc 821  df-tru 1338  df-fal 1341  df-nf 1441 This theorem is referenced by:  19.32dc  1659  finexdc  6840  ssfirab  6871  exfzdc  10121  nfsum1  11235  nfsum  11236  nfcprod1  11433  nfcprod  11434  zsupcllemstep  11813  infssuzex  11817  ctiunctlemudc  12138  iswomninnlem  13583
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