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Theorem tsan3 31796
Description: A Tseitin axiom for logical conjunction, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018.)
Assertion
Ref Expression
tsan3  |-  ( th 
->  ( ps  \/  -.  ( ph  /\  ps )
) )

Proof of Theorem tsan3
StepHypRef Expression
1 pm3.14 500 . . . 4  |-  ( ( -.  ph  \/  -.  ps )  ->  -.  ( ph  /\  ps ) )
21olcs 393 . . 3  |-  ( -. 
ps  ->  -.  ( ph  /\ 
ps ) )
32orri 374 . 2  |-  ( ps  \/  -.  ( ph  /\ 
ps ) )
43a1i 11 1  |-  ( th 
->  ( ps  \/  -.  ( ph  /\  ps )
) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 366    /\ wa 367
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 368  df-an 369
This theorem is referenced by:  tsna3  31799  ts3an3  31805  mpt2bi123f  31817  mptbi12f  31821
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