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Theorem notnot2ALTVD 37173
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 notnot2 115). 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. notnot2ALT 36744 is notnot2ALTVD 37173 without virtual deductions and was automatically derived from notnot2ALTVD 37173. Step i of the User's Proof corresponds to step i of the Fitch-style proof.
1::  |-  (. -.  -.  ph  ->.  -.  -.  ph ).
2::  |-  ( -.  -.  ph  ->  ( -.  ph  ->  -.  -.  -.  ph ) )
3:1:  |-  (. -.  -.  ph  ->.  ( -.  ph  ->  -.  -.  -.  ph ) ).
4::  |-  ( ( -.  ph  ->  -.  -.  -.  ph )  ->  ( -.  -.  ph  ->  ph ) )
5:3:  |-  (. -.  -.  ph  ->.  ( -.  -.  ph  ->  ph ) ).
6:5,1:  |-  (. -.  -.  ph  ->.  ph ).
qed:6:  |-  ( -.  -.  ph  ->  ph )
(Contributed by Alan Sare, 21-Apr-2013.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
notnot2ALTVD  |-  ( -. 
-.  ph  ->  ph )

Proof of Theorem notnot2ALTVD
StepHypRef Expression
1 idn1 36803 . . . . 5  |-  (.  -.  -.  ph  ->.  -.  -.  ph ).
2 pm2.21 111 . . . . 5  |-  ( -. 
-.  ph  ->  ( -. 
ph  ->  -.  -.  -.  ph ) )
31, 2e1a 36865 . . . 4  |-  (.  -.  -.  ph  ->.  ( -.  ph  ->  -.  -.  -.  ph ) ).
4 ax-3 8 . . . 4  |-  ( ( -.  ph  ->  -.  -.  -.  ph )  ->  ( -.  -.  ph  ->  ph )
)
53, 4e1a 36865 . . 3  |-  (.  -.  -.  ph  ->.  ( -.  -.  ph 
->  ph ) ).
6 id 23 . . 3  |-  ( ( -.  -.  ph  ->  ph )  ->  ( -.  -.  ph  ->  ph ) )
75, 1, 6e11 36926 . 2  |-  (.  -.  -.  ph  ->.  ph ).
87in1 36800 1  |-  ( -. 
-.  ph  ->  ph )
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 188  df-vd1 36799
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator