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Theorem nfdc 1620
 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 803 . 2 (DECID 𝜑 ↔ (𝜑 ∨ ¬ 𝜑))
2 nfdc.1 . . 3 𝑥𝜑
32nfn 1619 . . 3 𝑥 ¬ 𝜑
42, 3nfor 1536 . 2 𝑥(𝜑 ∨ ¬ 𝜑)
51, 4nfxfr 1433 1 𝑥DECID 𝜑
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   ∨ wo 680  DECID wdc 802  Ⅎwnf 1419 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-io 681  ax-5 1406  ax-gen 1408  ax-ie2 1453  ax-4 1470  ax-ial 1497 This theorem depends on definitions:  df-bi 116  df-dc 803  df-tru 1317  df-fal 1320  df-nf 1420 This theorem is referenced by:  19.32dc  1640  finexdc  6749  ssfirab  6774  exfzdc  9910  nfsum1  11017  nfsum  11018  zsupcllemstep  11486  infssuzex  11490  ctiunctlemudc  11793
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