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Theorem bj-nnfeai 34573
Description: Nonfreeness implies the equivalent of ax5ea 1920, inference form. (Contributed by BJ, 22-Sep-2024.)
Hypothesis
Ref Expression
bj-nnfeai.1 Ⅎ'𝑥𝜑
Assertion
Ref Expression
bj-nnfeai (∃𝑥𝜑 → ∀𝑥𝜑)

Proof of Theorem bj-nnfeai
StepHypRef Expression
1 bj-nnfeai.1 . 2 Ⅎ'𝑥𝜑
2 bj-nnfea 34571 . 2 (Ⅎ'𝑥𝜑 → (∃𝑥𝜑 → ∀𝑥𝜑))
31, 2ax-mp 5 1 (∃𝑥𝜑 → ∀𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1540  wex 1786  Ⅎ'wnnf 34560
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-an 400  df-bj-nnf 34561
This theorem is referenced by: (None)
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