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Theorem tsim2 29080
Description: A Tseitin axiom for logical implication, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018.)
Assertion
Ref Expression
tsim2  |-  ( th 
->  ( ph  \/  ( ph  ->  ps ) ) )

Proof of Theorem tsim2
StepHypRef Expression
1 orc 385 . . 3  |-  ( ph  ->  ( ph  \/  ( ph  ->  ps ) ) )
2 pm2.21 108 . . . 4  |-  ( -. 
ph  ->  ( ph  ->  ps ) )
32olcd 393 . . 3  |-  ( -. 
ph  ->  ( ph  \/  ( ph  ->  ps )
) )
41, 3pm2.61i 164 . 2  |-  ( ph  \/  ( ph  ->  ps ) )
54a1i 11 1  |-  ( th 
->  ( ph  \/  ( ph  ->  ps ) ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 368
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
This theorem is referenced by:  mpt2bi123f  29113  ac6s6  29122
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