Theorem bj-nf4 31768

Description: Alternate definition of df-bj-nf 31765. This definition uses only primitive symbols. (Contributed by BJ, 6-May-2019.)

Assertion

Ref	Expression
bj-nf4	⊢ (ℲℲ𝑥𝜑 ↔ (¬ ∀𝑥𝜑 → ∀𝑥 ¬ 𝜑))

Proof of Theorem bj-nf4

Step	Hyp	Ref	Expression
1		bj-nf3 31767	. 2 ⊢ (ℲℲ𝑥𝜑 ↔ (∀𝑥𝜑 ∨ ∀𝑥 ¬ 𝜑))
2		df-or 384	. 2 ⊢ ((∀𝑥𝜑 ∨ ∀𝑥 ¬ 𝜑) ↔ (¬ ∀𝑥𝜑 → ∀𝑥 ¬ 𝜑))
3	1, 2	bitri 263	1 ⊢ (ℲℲ𝑥𝜑 ↔ (¬ ∀𝑥𝜑 → ∀𝑥 ¬ 𝜑))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 195   ∨ wo 382  ∀wal 1473  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-or 384  df-ex 1696  df-bj-nf 31765

This theorem is referenced by: (None)