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Theorem bj-nndcALT 12993
Description: Alternate proof of nndc 836. (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
StepHypRef Expression
1 notnot 618 . . 3 𝜑 → ¬ ¬ ¬ 𝜑)
2 bj-nnor 12976 . . 3 (¬ ¬ (𝜑 ∨ ¬ 𝜑) ↔ (¬ 𝜑 → ¬ ¬ ¬ 𝜑))
31, 2mpbir 145 . 2 ¬ ¬ (𝜑 ∨ ¬ 𝜑)
4 df-dc 820 . . 3 (DECID 𝜑 ↔ (𝜑 ∨ ¬ 𝜑))
54notbii 657 . 2 DECID 𝜑 ↔ ¬ (𝜑 ∨ ¬ 𝜑))
63, 5mtbir 660 1 ¬ ¬ DECID 𝜑
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wo 697  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-dc 820
This theorem is referenced by: (None)
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