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Theorem nfdc 1565
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 754 . 2  |-  (DECID  ph  <->  ( ph  \/  -.  ph ) )
2 nfdc.1 . . 3  |-  F/ x ph
32nfn 1564 . . 3  |-  F/ x  -.  ph
42, 3nfor 1482 . 2  |-  F/ x
( ph  \/  -.  ph )
51, 4nfxfr 1379 1  |-  F/ xDECID  ph
Colors of variables: wff set class
Syntax hints:   -. wn 3    \/ wo 639  DECID wdc 753   F/wnf 1365
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-io 640  ax-5 1352  ax-gen 1354  ax-ie2 1399  ax-4 1416  ax-ial 1443
This theorem depends on definitions:  df-bi 114  df-dc 754  df-tru 1262  df-fal 1265  df-nf 1366
This theorem is referenced by:  19.32dc  1585
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