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Theorem notornotel1 29069
Description: A lemma for not-or-not elimination, in deduction form. (Contributed by Giovanni Mascellani, 19-Mar-2018.)
Hypothesis
Ref Expression
notornotel1.1  |-  ( ph  ->  -.  ( -.  ps  \/  ch ) )
Assertion
Ref Expression
notornotel1  |-  ( ph  ->  ps )

Proof of Theorem notornotel1
StepHypRef Expression
1 notornotel1.1 . 2  |-  ( ph  ->  -.  ( -.  ps  \/  ch ) )
2 ioran 490 . . . . 5  |-  ( -.  ( -.  ps  \/  ch )  <->  ( -.  -.  ps  /\  -.  ch )
)
32biimpi 194 . . . 4  |-  ( -.  ( -.  ps  \/  ch )  ->  ( -. 
-.  ps  /\  -.  ch ) )
4 simpl 457 . . . 4  |-  ( ( -.  -.  ps  /\  -.  ch )  ->  -.  -.  ps )
5 notnot2 112 . . . 4  |-  ( -. 
-.  ps  ->  ps )
63, 4, 53syl 20 . . 3  |-  ( -.  ( -.  ps  \/  ch )  ->  ps )
76imim2i 14 . 2  |-  ( (
ph  ->  -.  ( -.  ps  \/  ch ) )  ->  ( ph  ->  ps ) )
81, 7ax-mp 5 1  |-  ( ph  ->  ps )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 368    /\ wa 369
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:  notornotel2  29070  ac6s6  29155
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