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Theorem notnot2ALTVD 27478
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 27082 is notnot2ALTVD 27478 without virtual deductions and was automatically derived from notnot2ALTVD 27478. 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 27132 . . . . 5  |-  (.  -.  -.  ph  ->.  -.  -.  ph ).
2 pm2.21 102 . . . . 5  |-  ( -. 
-.  ph  ->  ( -. 
ph  ->  -.  -.  -.  ph ) )
31, 2e1_ 27186 . . . 4  |-  (.  -.  -.  ph  ->.  ( -.  ph  ->  -.  -.  -.  ph ) ).
4 ax-3 9 . . . 4  |-  ( ( -.  ph  ->  -.  -.  -.  ph )  ->  ( -.  -.  ph  ->  ph )
)
53, 4e1_ 27186 . . 3  |-  (.  -.  -.  ph  ->.  ( -.  -.  ph 
->  ph ) ).
6 id 21 . . 3  |-  ( ( -.  -.  ph  ->  ph )  ->  ( -.  -.  ph  ->  ph ) )
75, 1, 6e11 27247 . 2  |-  (.  -.  -.  ph  ->.  ph ).
87in1 27129 1  |-  ( -. 
-.  ph  ->  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-vd1 27128
  Copyright terms: Public domain W3C validator