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Theorem tsna1 32090
Description: A Tseitin axiom for logical incompatibility, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018.)
Assertion
Ref Expression
tsna1  |-  ( th 
->  ( ( -.  ph  \/  -.  ps )  \/ 
-.  ( ph  -/\  ps )
) )

Proof of Theorem tsna1
StepHypRef Expression
1 tsan1 32087 . 2  |-  ( th 
->  ( ( -.  ph  \/  -.  ps )  \/  ( ph  /\  ps ) ) )
2 notnot 292 . . . . 5  |-  ( (
ph  -/\  ps )  <->  -.  -.  ( ph  -/\  ps ) )
3 df-nan 1380 . . . . 5  |-  ( (
ph  -/\  ps )  <->  -.  ( ph  /\  ps ) )
42, 3bitr3i 254 . . . 4  |-  ( -. 
-.  ( ph  -/\  ps )  <->  -.  ( ph  /\  ps ) )
54con4bii 298 . . 3  |-  ( -.  ( ph  -/\  ps )  <->  (
ph  /\  ps )
)
65orbi2i 521 . 2  |-  ( ( ( -.  ph  \/  -.  ps )  \/  -.  ( ph  -/\  ps )
)  <->  ( ( -. 
ph  \/  -.  ps )  \/  ( ph  /\  ps ) ) )
71, 6sylibr 215 1  |-  ( th 
->  ( ( -.  ph  \/  -.  ps )  \/ 
-.  ( ph  -/\  ps )
) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 369    /\ wa 370    -/\ wnan 1379
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 188  df-or 371  df-an 372  df-nan 1380
This theorem is referenced by: (None)
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