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Theorem nfdc 1594
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 781 . 2  |-  (DECID  ph  <->  ( ph  \/  -.  ph ) )
2 nfdc.1 . . 3  |-  F/ x ph
32nfn 1593 . . 3  |-  F/ x  -.  ph
42, 3nfor 1511 . 2  |-  F/ x
( ph  \/  -.  ph )
51, 4nfxfr 1408 1  |-  F/ xDECID  ph
Colors of variables: wff set class
Syntax hints:   -. wn 3    \/ wo 664  DECID wdc 780   F/wnf 1394
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-io 665  ax-5 1381  ax-gen 1383  ax-ie2 1428  ax-4 1445  ax-ial 1472
This theorem depends on definitions:  df-bi 115  df-dc 781  df-tru 1292  df-fal 1295  df-nf 1395
This theorem is referenced by:  19.32dc  1614  finexdc  6608  ssfirab  6633  exfzdc  9639  nfsum1  10732  nfsum  10733  zsupcllemstep  11206  infssuzex  11210
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