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Theorem notnotrALTVD 41126
Description: The following User's Proof is a Natural Deduction Sequent Calculus transcription of the Fitch-style Natural Deduction proof of Theorem 5 of Section 14 of [Margaris] p. 59 (which is notnotr 132). The same proof may also be interpreted as a Virtual Deduction Hilbert-style axiomatic proof. It was completed automatically by the tools program completeusersproof.cmd, which invokes Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. notnotrALT 40740 is notnotrALTVD 41126 without virtual deductions and was automatically derived from notnotrALTVD 41126. Step i of the User's Proof corresponds to step i of the Fitch-style proof.
1:: (   ¬ ¬ 𝜑   ▶   ¬ ¬ 𝜑   )
2:: (¬ ¬ 𝜑 → (¬ 𝜑 → ¬ ¬ ¬ 𝜑))
3:1: (   ¬ ¬ 𝜑   ▶   𝜑 → ¬ ¬ ¬ 𝜑)   )
4:: ((¬ 𝜑 → ¬ ¬ ¬ 𝜑) → (¬ ¬ 𝜑 𝜑))
5:3: (   ¬ ¬ 𝜑   ▶   (¬ ¬ 𝜑𝜑)   )
6:5,1: (   ¬ ¬ 𝜑   ▶   𝜑   )
qed:6: (¬ ¬ 𝜑𝜑)
(Contributed by Alan Sare, 21-Apr-2013.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
notnotrALTVD (¬ ¬ 𝜑𝜑)

Proof of Theorem notnotrALTVD
StepHypRef Expression
1 idn1 40785 . . . . 5 (    ¬ ¬ 𝜑   ▶    ¬ ¬ 𝜑   )
2 pm2.21 123 . . . . 5 (¬ ¬ 𝜑 → (¬ 𝜑 → ¬ ¬ ¬ 𝜑))
31, 2e1a 40838 . . . 4 (    ¬ ¬ 𝜑   ▶   𝜑 → ¬ ¬ ¬ 𝜑)   )
4 con4 113 . . . 4 ((¬ 𝜑 → ¬ ¬ ¬ 𝜑) → (¬ ¬ 𝜑𝜑))
53, 4e1a 40838 . . 3 (    ¬ ¬ 𝜑   ▶   (¬ ¬ 𝜑𝜑)   )
6 id 22 . . 3 ((¬ ¬ 𝜑𝜑) → (¬ ¬ 𝜑𝜑))
75, 1, 6e11 40899 . 2 (    ¬ ¬ 𝜑   ▶   𝜑   )
87in1 40782 1 (¬ ¬ 𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 208  df-vd1 40781
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator