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Theorem ts3an3 32098
Description: A Tseitin axiom for triple logical conjunction, in deduction form. (Contributed by Giovanni Mascellani, 25-Mar-2018.)
Assertion
Ref Expression
ts3an3  |-  ( th 
->  ( ch  \/  -.  ( ph  /\  ps  /\  ch ) ) )

Proof of Theorem ts3an3
StepHypRef Expression
1 tsan3 32089 . 2  |-  ( th 
->  ( ch  \/  -.  ( ( ph  /\  ps )  /\  ch )
) )
2 df-3an 984 . . . 4  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ( ph  /\  ps )  /\  ch )
)
32notbii 297 . . 3  |-  ( -.  ( ph  /\  ps  /\ 
ch )  <->  -.  (
( ph  /\  ps )  /\  ch ) )
43orbi2i 521 . 2  |-  ( ( ch  \/  -.  ( ph  /\  ps  /\  ch ) )  <->  ( ch  \/  -.  ( ( ph  /\ 
ps )  /\  ch ) ) )
51, 4sylibr 215 1  |-  ( th 
->  ( ch  \/  -.  ( ph  /\  ps  /\  ch ) ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 369    /\ wa 370    /\ w3a 982
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-3an 984
This theorem is referenced by: (None)
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