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Theorem nfi 1704
Description: Deduce that 𝑥 is not free in 𝜑 from the definition. (Contributed by Wolf Lammen, 15-Sep-2021.)
Hypothesis
Ref Expression
nfi.1 (∃𝑥𝜑 → ∀𝑥𝜑)
Assertion
Ref Expression
nfi 𝑥𝜑

Proof of Theorem nfi
StepHypRef Expression
1 nfi.1 . 2 (∃𝑥𝜑 → ∀𝑥𝜑)
2 df-nf 1700 . 2 (Ⅎ𝑥𝜑 ↔ (∃𝑥𝜑 → ∀𝑥𝜑))
31, 2mpbir 219 1 𝑥𝜑
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1472  wex 1694  wnf 1698
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 195  df-nf 1700
This theorem is referenced by:  nfv  1829
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