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Theorem bj-nnfv 34159
Description: A non-occurring variable is nonfree in a formula. (Contributed by BJ, 28-Jul-2023.)
Assertion
Ref Expression
bj-nnfv Ⅎ'𝑥𝜑
Distinct variable group:   𝜑,𝑥

Proof of Theorem bj-nnfv
StepHypRef Expression
1 ax5e 1913 . 2 (∃𝑥𝜑𝜑)
2 ax-5 1911 . 2 (𝜑 → ∀𝑥𝜑)
3 df-bj-nnf 34132 . 2 (Ⅎ'𝑥𝜑 ↔ ((∃𝑥𝜑𝜑) ∧ (𝜑 → ∀𝑥𝜑)))
41, 2, 3mpbir2an 710 1 Ⅎ'𝑥𝜑
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1536  wex 1781  Ⅎ'wnnf 34131
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-5 1911
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-bj-nnf 34132
This theorem is referenced by: (None)
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