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Theorem nfd 1713
Description: Deduce that 𝑥 is not free in 𝜓 in a context. (Contributed by Wolf Lammen, 16-Sep-2021.)
Hypothesis
Ref Expression
nfd.1 (𝜑 → (∃𝑥𝜓 → ∀𝑥𝜓))
Assertion
Ref Expression
nfd (𝜑 → Ⅎ𝑥𝜓)

Proof of Theorem nfd
StepHypRef Expression
1 nfd.1 . 2 (𝜑 → (∃𝑥𝜓 → ∀𝑥𝜓))
2 df-nf 1707 . 2 (Ⅎ𝑥𝜓 ↔ (∃𝑥𝜓 → ∀𝑥𝜓))
31, 2sylibr 224 1 (𝜑 → Ⅎ𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1478  wex 1701  wnf 1705
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-nf 1707
This theorem is referenced by:  nfimdOLDOLD  1821  nf5-1  2020  axc16nf  2133  nfald  2162
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