Theorem bj-nnfth 37410

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

Step	Hyp	Ref	Expression
1		bj-nnftht 37409	. 2 ⊢ ((𝜑 ∧ ∀𝑥𝜑) → Ⅎ'𝑥𝜑)
2		bj-nnfth.1	. 2 ⊢ 𝜑
3	1, 2	bj-mpgs 37244	1 ⊢ Ⅎ'𝑥𝜑

This proof depends on syntax axioms:  Ⅎ'wnnf 37392

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828

This proof depends on definitions:  df-bi 210  df-an 402  df-bj-nnf 37393

This theorem is used by:  bj-nnfnth  37417