Theorem bj-nftht 31769

Description: Closed form of nfth 1718. (Contributed by BJ, 6-May-2019.)

Assertion

Ref	Expression
bj-nftht	⊢ (∀𝑥𝜑 → ℲℲ𝑥𝜑)

Proof of Theorem bj-nftht

Step	Hyp	Ref	Expression
1		ax-1 6	. 2 ⊢ (∀𝑥𝜑 → (∃𝑥𝜑 → ∀𝑥𝜑))
2		df-bj-nf 31765	. 2 ⊢ (ℲℲ𝑥𝜑 ↔ (∃𝑥𝜑 → ∀𝑥𝜑))
3	1, 2	sylibr 223	1 ⊢ (∀𝑥𝜑 → ℲℲ𝑥𝜑)

Syntax hints:   → wi 4  ∀wal 1473  ∃wex 1695  ℲℲwnff 31764

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

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

This theorem is referenced by:  bj-nfth  31772