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Theorem nfd 1792
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 1786 . 2 (Ⅎ𝑥𝜓 ↔ (∃𝑥𝜓 → ∀𝑥𝜓))
31, 2sylibr 237 1 (𝜑 → Ⅎ𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1536  wex 1781  wnf 1785
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 210  df-nf 1786
This theorem is referenced by:  nftht  1794  nfntht  1795  nfimd  1896  nf5-1  2150  axc16nf  2265  nfald  2348  nfeqf2  2396  bj-nfald  34445
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