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Theorem tsan2 29077
Description: A Tseitin axiom for logical conjunction, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018.)
Assertion
Ref Expression
tsan2  |-  ( th 
->  ( ph  \/  -.  ( ph  /\  ps )
) )

Proof of Theorem tsan2
StepHypRef Expression
1 orc 385 . . 3  |-  ( ph  ->  ( ph  \/  -.  ( ph  /\  ps )
) )
2 orc 385 . . . . 5  |-  ( -. 
ph  ->  ( -.  ph  \/  -.  ps ) )
3 pm3.14 502 . . . . 5  |-  ( ( -.  ph  \/  -.  ps )  ->  -.  ( ph  /\  ps ) )
42, 3syl 16 . . . 4  |-  ( -. 
ph  ->  -.  ( ph  /\ 
ps ) )
54olcd 393 . . 3  |-  ( -. 
ph  ->  ( ph  \/  -.  ( ph  /\  ps ) ) )
61, 5pm2.61i 164 . 2  |-  ( ph  \/  -.  ( ph  /\  ps ) )
76a1i 11 1  |-  ( th 
->  ( ph  \/  -.  ( 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:  tsna2  29080  ts3an2  29086  mpt2bi123f  29099  mptbi12f  29103
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