Theorem bj-nndcALT 15414

Description: Alternate proof of nndc 852. (Proof modification is discouraged.) (New usage is discouraged.) (Contributed by BJ, 9-Oct-2019.)

Assertion

Ref	Expression
bj-nndcALT	⊢ ¬ ¬ DECID 𝜑

Proof of Theorem bj-nndcALT

Step	Hyp	Ref	Expression
1		notnot 630	. . 3 ⊢ (¬ 𝜑 → ¬ ¬ ¬ 𝜑)
2		bj-nnor 15390	. . 3 ⊢ (¬ ¬ (𝜑 ∨ ¬ 𝜑) ↔ (¬ 𝜑 → ¬ ¬ ¬ 𝜑))
3	1, 2	mpbir 146	. 2 ⊢ ¬ ¬ (𝜑 ∨ ¬ 𝜑)
4		df-dc 836	. . 3 ⊢ (DECID 𝜑 ↔ (𝜑 ∨ ¬ 𝜑))
5	4	notbii 669	. 2 ⊢ (¬ DECID 𝜑 ↔ ¬ (𝜑 ∨ ¬ 𝜑))
6	3, 5	mtbir 672	1 ⊢ ¬ ¬ DECID 𝜑

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 709  DECID wdc 835

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710

This theorem depends on definitions:  df-bi 117  df-dc 836

This theorem is referenced by: (None)