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Theorem notnot2ALTVD 28779
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 106). 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 O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. notnot2ALT 28366 is notnot2ALTVD 28779 without virtual deductions and was automatically derived from notnot2ALTVD 28779. 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 28417 . . . . 5  |-  (.  -.  -.  ph  ->.  -.  -.  ph ).
2 pm2.21 102 . . . . 5  |-  ( -. 
-.  ph  ->  ( -. 
ph  ->  -.  -.  -.  ph ) )
31, 2e1_ 28480 . . . 4  |-  (.  -.  -.  ph  ->.  ( -.  ph  ->  -.  -.  -.  ph ) ).
4 ax-3 7 . . . 4  |-  ( ( -.  ph  ->  -.  -.  -.  ph )  ->  ( -.  -.  ph  ->  ph )
)
53, 4e1_ 28480 . . 3  |-  (.  -.  -.  ph  ->.  ( -.  -.  ph 
->  ph ) ).
6 id 20 . . 3  |-  ( ( -.  -.  ph  ->  ph )  ->  ( -.  -.  ph  ->  ph ) )
75, 1, 6e11 28541 . 2  |-  (.  -.  -.  ph  ->.  ph ).
87in1 28414 1  |-  ( -. 
-.  ph  ->  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178  df-vd1 28413
  Copyright terms: Public domain W3C validator