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Theorem nfdc 1546
 Description: If x is not free in φ, it is not free in DECID φ. (Contributed by Jim Kingdon, 11-Mar-2018.)
Hypothesis
Ref Expression
nfdc.1 xφ
Assertion
Ref Expression
nfdc xDECID φ

Proof of Theorem nfdc
StepHypRef Expression
1 df-dc 742 . 2 (DECID φ ↔ (φ ¬ φ))
2 nfdc.1 . . 3 xφ
32nfn 1545 . . 3 x ¬ φ
42, 3nfor 1463 . 2 x(φ ¬ φ)
51, 4nfxfr 1360 1 xDECID φ
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   ∨ wo 628  DECID wdc 741  Ⅎwnf 1346 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629  ax-5 1333  ax-gen 1335  ax-ie2 1380  ax-4 1397  ax-ial 1424 This theorem depends on definitions:  df-bi 110  df-dc 742  df-tru 1245  df-fal 1248  df-nf 1347 This theorem is referenced by:  19.32dc  1566
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