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Theorem nfdc 1622
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 805 . 2 (DECID 𝜑 ↔ (𝜑 ∨ ¬ 𝜑))
2 nfdc.1 . . 3 𝑥𝜑
32nfn 1621 . . 3 𝑥 ¬ 𝜑
42, 3nfor 1538 . 2 𝑥(𝜑 ∨ ¬ 𝜑)
51, 4nfxfr 1435 1 𝑥DECID 𝜑
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wo 682  DECID wdc 804  wnf 1421
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 588  ax-in2 589  ax-io 683  ax-5 1408  ax-gen 1410  ax-ie2 1455  ax-4 1472  ax-ial 1499
This theorem depends on definitions:  df-bi 116  df-dc 805  df-tru 1319  df-fal 1322  df-nf 1422
This theorem is referenced by:  19.32dc  1642  finexdc  6764  ssfirab  6790  exfzdc  9985  nfsum1  11093  nfsum  11094  zsupcllemstep  11565  infssuzex  11569  ctiunctlemudc  11877
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