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Theorem nfri 1705
Description: Consequence of the definition of not-free. (Contributed by Wolf Lammen, 16-Sep-2021.)
Hypothesis
Ref Expression
nfri.1 𝑥𝜑
Assertion
Ref Expression
nfri (∃𝑥𝜑 → ∀𝑥𝜑)

Proof of Theorem nfri
StepHypRef Expression
1 nfri.1 . 2 𝑥𝜑
2 df-nf 1700 . 2 (Ⅎ𝑥𝜑 ↔ (∃𝑥𝜑 → ∀𝑥𝜑))
31, 2mpbi 218 1 (∃𝑥𝜑 → ∀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: (None)
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