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Theorem nfdc 1652
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 830 . 2 (DECID 𝜑 ↔ (𝜑 ∨ ¬ 𝜑))
2 nfdc.1 . . 3 𝑥𝜑
32nfn 1651 . . 3 𝑥 ¬ 𝜑
42, 3nfor 1567 . 2 𝑥(𝜑 ∨ ¬ 𝜑)
51, 4nfxfr 1467 1 𝑥DECID 𝜑
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wo 703  DECID wdc 829  wnf 1453
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 609  ax-in2 610  ax-io 704  ax-5 1440  ax-gen 1442  ax-ie2 1487  ax-4 1503  ax-ial 1527
This theorem depends on definitions:  df-bi 116  df-dc 830  df-tru 1351  df-fal 1354  df-nf 1454
This theorem is referenced by:  19.32dc  1672  finexdc  6880  ssfirab  6911  dcfi  6958  exfzdc  10196  nfsum1  11319  nfsum  11320  nfcprod1  11517  nfcprod  11518  zsupcllemstep  11900  infssuzex  11904  nnwosdc  11994  ctiunctlemudc  12392  iswomninnlem  14081
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