Theorem bj-nfnth 31774

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

Hypothesis

Ref	Expression
bj-nfnth.1	⊢ ¬ 𝜑

Assertion

Ref	Expression
bj-nfnth	⊢ ℲℲ𝑥𝜑

Proof of Theorem bj-nfnth

Step	Hyp	Ref	Expression
1		bj-nfntht2 31771	. 2 ⊢ (∀𝑥 ¬ 𝜑 → ℲℲ𝑥𝜑)
2		bj-nfnth.1	. 2 ⊢ ¬ 𝜑
3	1, 2	mpg 1715	1 ⊢ ℲℲ𝑥𝜑

Syntax hints:  ¬ wn 3  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-or 384  df-ex 1696  df-bj-nf 31765

This theorem is referenced by:  bj-nffal  31775