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Theorem tsbi1 29112
Description: A Tseitin axiom for logical biimplication, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018.)
Assertion
Ref Expression
tsbi1  |-  ( th 
->  ( ( -.  ph  \/  -.  ps )  \/  ( ph  <->  ps )
) )

Proof of Theorem tsbi1
StepHypRef Expression
1 pm5.1 853 . . . 4  |-  ( (
ph  /\  ps )  ->  ( ph  <->  ps )
)
21olcd 393 . . 3  |-  ( (
ph  /\  ps )  ->  ( ( -.  ph  \/  -.  ps )  \/  ( ph  <->  ps )
) )
3 pm3.13 501 . . . 4  |-  ( -.  ( ph  /\  ps )  ->  ( -.  ph  \/  -.  ps ) )
43orcd 392 . . 3  |-  ( -.  ( ph  /\  ps )  ->  ( ( -. 
ph  \/  -.  ps )  \/  ( ph  <->  ps )
) )
52, 4pm2.61i 164 . 2  |-  ( ( -.  ph  \/  -.  ps )  \/  ( ph 
<->  ps ) )
65a1i 11 1  |-  ( th 
->  ( ( -.  ph  \/  -.  ps )  \/  ( ph  <->  ps )
) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 184    \/ 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:  tsxo1  29116  mpt2bi123f  29143  mptbi12f  29147  ac6s6  29152
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