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Theorem bj-nnfth 34932
Description: A variable is nonfree in a theorem, inference form. (Contributed by BJ, 28-Jul-2023.)
Hypothesis
Ref Expression
bj-nnfth.1 𝜑
Assertion
Ref Expression
bj-nnfth Ⅎ'𝑥𝜑

Proof of Theorem bj-nnfth
StepHypRef Expression
1 bj-nnfth.1 . 2 𝜑
2 bj-nnftht 34931 . 2 ((𝜑 ∧ ∀𝑥𝜑) → Ⅎ'𝑥𝜑)
31, 2bj-mpgs 34799 1 Ⅎ'𝑥𝜑
Colors of variables: wff setvar class
Syntax hints:  Ⅎ'wnnf 34913
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798
This theorem depends on definitions:  df-bi 206  df-an 397  df-bj-nnf 34914
This theorem is referenced by:  bj-nnfnth  34933
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