Theorem bj-nnst 12967

Description: Double negation of stability of a formula. Intuitionistic logic refutes unstability (but does not prove stability) of any formula. (Contributed by BJ, 9-Oct-2019.)

Assertion

Ref	Expression
bj-nnst	⊢ ¬ ¬ STAB 𝜑

Proof of Theorem bj-nnst

Step	Hyp	Ref	Expression
1		nndc 836	. 2 ⊢ ¬ ¬ DECID 𝜑
2		dcstab 829	. . 3 ⊢ (DECID 𝜑 → STAB 𝜑)
3	2	con3i 621	. 2 ⊢ (¬ STAB 𝜑 → ¬ DECID 𝜑)
4	1, 3	mto 651	1 ⊢ ¬ ¬ STAB 𝜑

Syntax hints:  ¬ wn 3  STAB wstab 815  DECID wdc 819

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698

This theorem depends on definitions:  df-bi 116  df-stab 816  df-dc 820

This theorem is referenced by:  bj-dcst  12970  bj-stst  12971