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Theorem dcnnOLD 835
 Description: Obsolete proof of dcnnOLD 835 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 ¬ 𝜑DECID ¬ ¬ 𝜑)

Proof of Theorem dcnnOLD
StepHypRef Expression
1 notnotnot 624 . . . 4 (¬ ¬ ¬ 𝜑 ↔ ¬ 𝜑)
21orbi2i 752 . . 3 ((¬ ¬ 𝜑 ∨ ¬ ¬ ¬ 𝜑) ↔ (¬ ¬ 𝜑 ∨ ¬ 𝜑))
3 orcom 718 . . 3 ((¬ ¬ 𝜑 ∨ ¬ 𝜑) ↔ (¬ 𝜑 ∨ ¬ ¬ 𝜑))
42, 3bitri 183 . 2 ((¬ ¬ 𝜑 ∨ ¬ ¬ ¬ 𝜑) ↔ (¬ 𝜑 ∨ ¬ ¬ 𝜑))
5 df-dc 821 . 2 (DECID ¬ ¬ 𝜑 ↔ (¬ ¬ 𝜑 ∨ ¬ ¬ ¬ 𝜑))
6 df-dc 821 . 2 (DECID ¬ 𝜑 ↔ (¬ 𝜑 ∨ ¬ ¬ 𝜑))
74, 5, 63bitr4ri 212 1 (DECID ¬ 𝜑DECID ¬ ¬ 𝜑)
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   ↔ wb 104   ∨ wo 698  DECID wdc 820 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 821 This theorem is referenced by: (None)
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