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Theorem nfdc 1670
Description: If  x is not free in  ph, it is not free in DECID  ph. (Contributed by Jim Kingdon, 11-Mar-2018.)
Hypothesis
Ref Expression
nfdc.1  |-  F/ x ph
Assertion
Ref Expression
nfdc  |-  F/ xDECID  ph

Proof of Theorem nfdc
StepHypRef Expression
1 df-dc 836 . 2  |-  (DECID  ph  <->  ( ph  \/  -.  ph ) )
2 nfdc.1 . . 3  |-  F/ x ph
32nfn 1669 . . 3  |-  F/ x  -.  ph
42, 3nfor 1585 . 2  |-  F/ x
( ph  \/  -.  ph )
51, 4nfxfr 1485 1  |-  F/ xDECID  ph
Colors of variables: wff set class
Syntax hints:   -. wn 3    \/ wo 709  DECID wdc 835   F/wnf 1471
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710  ax-5 1458  ax-gen 1460  ax-ie2 1505  ax-4 1521  ax-ial 1545
This theorem depends on definitions:  df-bi 117  df-dc 836  df-tru 1367  df-fal 1370  df-nf 1472
This theorem is referenced by:  19.32dc  1690  finexdc  6929  ssfirab  6961  dcfi  7009  exfzdc  10269  nfsum1  11395  nfsum  11396  nfcprod1  11593  nfcprod  11594  zsupcllemstep  11977  infssuzex  11981  nnwosdc  12071  ctiunctlemudc  12487  iswomninnlem  15251
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