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Theorem notnot2ALT2 27836
Description: Converse of double negation. Theorem *2.14 of [WhiteheadRussell] p. 102. Proof derived by completeusersproof.c from User's Proof in VirtualDeductionProofs.txt. (Contributed by Alan Sare, 11-Sep-2016.)
Assertion
Ref Expression
notnot2ALT2  |-  ( -. 
-.  ph  ->  ph )

Proof of Theorem notnot2ALT2
StepHypRef Expression
1 id 21 . . 3  |-  ( -. 
-.  ph  ->  -.  -.  ph )
2 pm2.21 102 . . . . 5  |-  ( -. 
-.  ph  ->  ( -. 
ph  ->  -.  -.  -.  ph ) )
31, 2syl 17 . . . 4  |-  ( -. 
-.  ph  ->  ( -. 
ph  ->  -.  -.  -.  ph ) )
4 ax-3 9 . . . 4  |-  ( ( -.  ph  ->  -.  -.  -.  ph )  ->  ( -.  -.  ph  ->  ph )
)
53, 4syl 17 . . 3  |-  ( -. 
-.  ph  ->  ( -. 
-.  ph  ->  ph )
)
6 pm3.35 573 . . 3  |-  ( ( -.  -.  ph  /\  ( -.  -.  ph  ->  ph ) )  ->  ph )
71, 5, 6syl2anc 645 . 2  |-  ( -. 
-.  ph  ->  ph )
87idi 2 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-an 362
  Copyright terms: Public domain W3C validator