Theorem dcnnOLD 849

Description: Obsolete proof of dcnnOLD 849 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 634	. . . 4 ⊢ (¬ ¬ ¬ 𝜑 ↔ ¬ 𝜑)
2	1	orbi2i 762	. . 3 ⊢ ((¬ ¬ 𝜑 ∨ ¬ ¬ ¬ 𝜑) ↔ (¬ ¬ 𝜑 ∨ ¬ 𝜑))
3		orcom 728	. . 3 ⊢ ((¬ ¬ 𝜑 ∨ ¬ 𝜑) ↔ (¬ 𝜑 ∨ ¬ ¬ 𝜑))
4	2, 3	bitri 184	. 2 ⊢ ((¬ ¬ 𝜑 ∨ ¬ ¬ ¬ 𝜑) ↔ (¬ 𝜑 ∨ ¬ ¬ 𝜑))
5		df-dc 835	. 2 ⊢ (DECID ¬ ¬ 𝜑 ↔ (¬ ¬ 𝜑 ∨ ¬ ¬ ¬ 𝜑))
6		df-dc 835	. 2 ⊢ (DECID ¬ 𝜑 ↔ (¬ 𝜑 ∨ ¬ ¬ 𝜑))
7	4, 5, 6	3bitr4ri 213	1 ⊢ (DECID ¬ 𝜑 ↔ DECID ¬ ¬ 𝜑)

Syntax hints:  ¬ wn 3   ↔ wb 105   ∨ wo 708  DECID wdc 834

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 614  ax-in2 615  ax-io 709

This theorem depends on definitions:  df-bi 117  df-dc 835

This theorem is referenced by: (None)