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Theorem notnot2ALTVD 28691
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 104). 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 28292 is notnot2ALTVD 28691 without virtual deductions and was automatically derived from notnot2ALTVD 28691. 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 28342 . . . . 5  |-  (.  -.  -.  ph  ->.  -.  -.  ph ).
2 pm2.21 100 . . . . 5  |-  ( -. 
-.  ph  ->  ( -. 
ph  ->  -.  -.  -.  ph ) )
31, 2e1_ 28399 . . . 4  |-  (.  -.  -.  ph  ->.  ( -.  ph  ->  -.  -.  -.  ph ) ).
4 ax-3 7 . . . 4  |-  ( ( -.  ph  ->  -.  -.  -.  ph )  ->  ( -.  -.  ph  ->  ph )
)
53, 4e1_ 28399 . . 3  |-  (.  -.  -.  ph  ->.  ( -.  -.  ph 
->  ph ) ).
6 id 19 . . 3  |-  ( ( -.  -.  ph  ->  ph )  ->  ( -.  -.  ph  ->  ph ) )
75, 1, 6e11 28460 . 2  |-  (.  -.  -.  ph  ->.  ph ).
87in1 28339 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 177  df-vd1 28338
  Copyright terms: Public domain W3C validator