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Theorem notornotel2 29023
Description: A lemma for not-or-not elimination, in deduction form. (Contributed by Giovanni Mascellani, 19-Mar-2018.)
Hypothesis
Ref Expression
notornotel2.1  |-  ( ph  ->  -.  ( ps  \/  -.  ch ) )
Assertion
Ref Expression
notornotel2  |-  ( ph  ->  ch )

Proof of Theorem notornotel2
StepHypRef Expression
1 notornotel2.1 . . 3  |-  ( ph  ->  -.  ( ps  \/  -.  ch ) )
2 orcom 387 . . . 4  |-  ( ( -.  ch  \/  ps ) 
<->  ( ps  \/  -.  ch ) )
32notbii 296 . . 3  |-  ( -.  ( -.  ch  \/  ps )  <->  -.  ( ps  \/  -.  ch ) )
41, 3sylibr 212 . 2  |-  ( ph  ->  -.  ( -.  ch  \/  ps ) )
54notornotel1 29022 1  |-  ( ph  ->  ch )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 368
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 185  df-or 370  df-an 371
This theorem is referenced by:  ac6s6  29108
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