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Theorem notatnand 27276
Description: Do not use. Use intnanr instead. Given not a, there exists a proof for not (a and b). (Contributed by Jarvin Udandy, 31-Aug-2016.)
Hypothesis
Ref Expression
notatnand.1  |-  -.  ph
Assertion
Ref Expression
notatnand  |-  -.  ( ph  /\  ps )

Proof of Theorem notatnand
StepHypRef Expression
1 notatnand.1 . . 3  |-  -.  ph
2 orc 374 . . 3  |-  ( -. 
ph  ->  ( -.  ph  \/  -.  ps ) )
31, 2ax-mp 8 . 2  |-  ( -. 
ph  \/  -.  ps )
4 ianor 474 . . . 4  |-  ( -.  ( ph  /\  ps ) 
<->  ( -.  ph  \/  -.  ps ) )
5 bicom 191 . . . . 5  |-  ( ( -.  ( ph  /\  ps )  <->  ( -.  ph  \/  -.  ps ) )  <-> 
( ( -.  ph  \/  -.  ps )  <->  -.  ( ph  /\  ps ) ) )
65biimpi 186 . . . 4  |-  ( ( -.  ( ph  /\  ps )  <->  ( -.  ph  \/  -.  ps ) )  ->  ( ( -. 
ph  \/  -.  ps )  <->  -.  ( ph  /\  ps ) ) )
74, 6ax-mp 8 . . 3  |-  ( ( -.  ph  \/  -.  ps )  <->  -.  ( ph  /\ 
ps ) )
87biimpi 186 . 2  |-  ( ( -.  ph  \/  -.  ps )  ->  -.  ( ph  /\  ps ) )
93, 8ax-mp 8 1  |-  -.  ( ph  /\  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176    \/ wo 357    /\ wa 358
This theorem is referenced by:  dandysum2p2e4  27355
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-or 359  df-an 360
  Copyright terms: Public domain W3C validator