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Theorem bj-nnfea 36119
Description: Nonfreeness implies the equivalent of ax5ea 1908. (Contributed by BJ, 28-Jul-2023.)
Assertion
Ref Expression
bj-nnfea (Ⅎ'𝑥𝜑 → (∃𝑥𝜑 → ∀𝑥𝜑))

Proof of Theorem bj-nnfea
StepHypRef Expression
1 bj-nnfe 36116 . 2 (Ⅎ'𝑥𝜑 → (∃𝑥𝜑𝜑))
2 bj-nnfa 36113 . 2 (Ⅎ'𝑥𝜑 → (𝜑 → ∀𝑥𝜑))
31, 2syld 47 1 (Ⅎ'𝑥𝜑 → (∃𝑥𝜑 → ∀𝑥𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1531  wex 1773  Ⅎ'wnnf 36108
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 206  df-an 396  df-bj-nnf 36109
This theorem is referenced by:  bj-nnfead  36120  bj-nnfeai  36121  bj-nnfnfTEMP  36123  bj-dfnnf3  36142
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