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Theorem tsbi2 32334
Description: A Tseitin axiom for logical biimplication, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018.)
Assertion
Ref Expression
tsbi2  |-  ( th 
->  ( ( ph  \/  ps )  \/  ( ph 
<->  ps ) ) )

Proof of Theorem tsbi2
StepHypRef Expression
1 pm5.21 867 . . . 4  |-  ( ( -.  ph  /\  -.  ps )  ->  ( ph  <->  ps )
)
21olcd 395 . . 3  |-  ( ( -.  ph  /\  -.  ps )  ->  ( ( ph  \/  ps )  \/  ( ph 
<->  ps ) ) )
3 pm4.57 500 . . . . 5  |-  ( -.  ( -.  ph  /\  -.  ps )  <->  ( ph  \/  ps ) )
43biimpi 198 . . . 4  |-  ( -.  ( -.  ph  /\  -.  ps )  ->  ( ph  \/  ps ) )
54orcd 394 . . 3  |-  ( -.  ( -.  ph  /\  -.  ps )  ->  (
( ph  \/  ps )  \/  ( ph  <->  ps ) ) )
62, 5pm2.61i 168 . 2  |-  ( (
ph  \/  ps )  \/  ( ph  <->  ps )
)
76a1i 11 1  |-  ( th 
->  ( ( ph  \/  ps )  \/  ( ph 
<->  ps ) ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 188    \/ wo 370    /\ wa 371
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 189  df-or 372  df-an 373
This theorem is referenced by:  tsxo2  32338  mpt2bi123f  32364  mptbi12f  32368  ac6s6  32373
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