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Theorem tsbi2 30781
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 pm5.21 856 . . . 4  |-  ( ( -.  ph  /\  -.  ps )  ->  ( ph  <->  ps )
)
21olcd 391 . . 3  |-  ( ( -.  ph  /\  -.  ps )  ->  ( ( ph  \/  ps )  \/  ( ph 
<->  ps ) ) )
3 pm4.57 495 . . . . 5  |-  ( -.  ( -.  ph  /\  -.  ps )  <->  ( ph  \/  ps ) )
43biimpi 194 . . . 4  |-  ( -.  ( -.  ph  /\  -.  ps )  ->  ( ph  \/  ps ) )
54orcd 390 . . 3  |-  ( -.  ( -.  ph  /\  -.  ps )  ->  (
( ph  \/  ps )  \/  ( ph  <->  ps ) ) )
62, 5pm2.61i 164 . 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 184    \/ 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:  tsxo2  30785  mpt2bi123f  30811  mptbi12f  30815  ac6s6  30820
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