Theorem bj-nfth 31772

Description: Any variable is not free in a theorem. (Contributed by BJ, 6-May-2019.)

Hypothesis

Ref	Expression
bj-nfth.1	⊢ 𝜑

Assertion

Ref	Expression
bj-nfth	⊢ ℲℲ𝑥𝜑

Proof of Theorem bj-nfth

Step	Hyp	Ref	Expression
1		bj-nftht 31769	. 2 ⊢ (∀𝑥𝜑 → ℲℲ𝑥𝜑)
2		bj-nfth.1	. 2 ⊢ 𝜑
3	1, 2	mpg 1715	1 ⊢ ℲℲ𝑥𝜑

Syntax hints:  ℲℲwnff 31764

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713

This theorem depends on definitions:  df-bi 196  df-bj-nf 31765

This theorem is referenced by:  bj-nftru  31773