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Theorem nfdc 1565
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 754 . 2 (DECID 𝜑 ↔ (𝜑 ∨ ¬ 𝜑))
2 nfdc.1 . . 3 𝑥𝜑
32nfn 1564 . . 3 𝑥 ¬ 𝜑
42, 3nfor 1482 . 2 𝑥(𝜑 ∨ ¬ 𝜑)
51, 4nfxfr 1379 1 𝑥DECID 𝜑
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wo 639  DECID wdc 753  wnf 1365
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-io 640  ax-5 1352  ax-gen 1354  ax-ie2 1399  ax-4 1416  ax-ial 1443
This theorem depends on definitions:  df-bi 114  df-dc 754  df-tru 1262  df-fal 1265  df-nf 1366
This theorem is referenced by:  19.32dc  1585
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