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Theorem tsan1 29120
Description: A Tseitin axiom for logical conjunction, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018.)
Assertion
Ref Expression
tsan1  |-  ( th 
->  ( ( -.  ph  \/  -.  ps )  \/  ( ph  /\  ps ) ) )

Proof of Theorem tsan1
StepHypRef Expression
1 pm3.12 500 . 2  |-  ( ( -.  ph  \/  -.  ps )  \/  ( ph  /\  ps ) )
21a1i 11 1  |-  ( th 
->  ( ( -.  ph  \/  -.  ps )  \/  ( 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:  tsna1  29123  ts3an1  29129  mpt2bi123f  29143  mptbi12f  29147
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