Theorem bj-nfv 31806

Description: A non-occurring variable is semantically non-free. (Contributed by BJ, 6-May-2019.)

Assertion

Ref	Expression
bj-nfv	⊢ ℲℲ𝑥𝜑

Distinct variable group:   𝜑,𝑥

Proof of Theorem bj-nfv

Step	Hyp	Ref	Expression
1		bj-ax5ea 31805	. 2 ⊢ (∃𝑥𝜑 → ∀𝑥𝜑)
2		df-bj-nf 31765	. 2 ⊢ (ℲℲ𝑥𝜑 ↔ (∃𝑥𝜑 → ∀𝑥𝜑))
3	1, 2	mpbir 220	1 ⊢ 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  ax-5 1827

This theorem depends on definitions:  df-bi 196  df-ex 1696  df-bj-nf 31765

This theorem is referenced by: (None)