Theorem dcnnOLD 839

Description: Obsolete proof of dcnnOLD 839 as of 25-Nov-2023. (Contributed by David A. Wheeler, 6-Dec-2018.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
dcnnOLD	⊢ (DECID ¬ 𝜑 ↔ DECID ¬ ¬ 𝜑)

Proof of Theorem dcnnOLD

Step	Hyp	Ref	Expression
1		notnotnot 624	. . . 4 ⊢ (¬ ¬ ¬ 𝜑 ↔ ¬ 𝜑)
2	1	orbi2i 752	. . 3 ⊢ ((¬ ¬ 𝜑 ∨ ¬ ¬ ¬ 𝜑) ↔ (¬ ¬ 𝜑 ∨ ¬ 𝜑))
3		orcom 718	. . 3 ⊢ ((¬ ¬ 𝜑 ∨ ¬ 𝜑) ↔ (¬ 𝜑 ∨ ¬ ¬ 𝜑))
4	2, 3	bitri 183	. 2 ⊢ ((¬ ¬ 𝜑 ∨ ¬ ¬ ¬ 𝜑) ↔ (¬ 𝜑 ∨ ¬ ¬ 𝜑))
5		df-dc 825	. 2 ⊢ (DECID ¬ ¬ 𝜑 ↔ (¬ ¬ 𝜑 ∨ ¬ ¬ ¬ 𝜑))
6		df-dc 825	. 2 ⊢ (DECID ¬ 𝜑 ↔ (¬ 𝜑 ∨ ¬ ¬ 𝜑))
7	4, 5, 6	3bitr4ri 212	1 ⊢ (DECID ¬ 𝜑 ↔ DECID ¬ ¬ 𝜑)

Syntax hints:  ¬ wn 3   ↔ wb 104   ∨ wo 698  DECID wdc 824

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 604  ax-in2 605  ax-io 699

This theorem depends on definitions:  df-bi 116  df-dc 825

This theorem is referenced by: (None)