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Theorem nfdc 1670
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 836 . 2 (DECID 𝜑 ↔ (𝜑 ∨ ¬ 𝜑))
2 nfdc.1 . . 3 𝑥𝜑
32nfn 1669 . . 3 𝑥 ¬ 𝜑
42, 3nfor 1585 . 2 𝑥(𝜑 ∨ ¬ 𝜑)
51, 4nfxfr 1485 1 𝑥DECID 𝜑
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wo 709  DECID wdc 835  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  6949  ssfirab  6981  dcfi  7030  exfzdc  10297  nfsum1  11489  nfsum  11490  nfcprod1  11687  nfcprod  11688  zsupcllemstep  12072  infssuzex  12076  nnwosdc  12166  ctiunctlemudc  12584  iswomninnlem  15484
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