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Theorem tsbi4 29115
Description: A Tseitin axiom for logical biimplication, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018.)
Assertion
Ref Expression
tsbi4  |-  ( th 
->  ( ( -.  ph  \/  ps )  \/  -.  ( ph  <->  ps ) ) )

Proof of Theorem tsbi4
StepHypRef Expression
1 tsbi3 29114 . 2  |-  ( th 
->  ( ( ps  \/  -.  ph )  \/  -.  ( ps  <->  ph ) ) )
2 orcom 387 . . . 4  |-  ( ( ps  \/  -.  ph ) 
<->  ( -.  ph  \/  ps ) )
32orbi1i 520 . . 3  |-  ( ( ( ps  \/  -.  ph )  \/  -.  ( ps 
<-> 
ph ) )  <->  ( ( -.  ph  \/  ps )  \/  -.  ( ps  <->  ph ) ) )
4 bicom 200 . . . . 5  |-  ( ( ps  <->  ph )  <->  ( ph  <->  ps ) )
54notbii 296 . . . 4  |-  ( -.  ( ps  <->  ph )  <->  -.  ( ph 
<->  ps ) )
65orbi2i 519 . . 3  |-  ( ( ( -.  ph  \/  ps )  \/  -.  ( ps  <->  ph ) )  <->  ( ( -.  ph  \/  ps )  \/  -.  ( ph  <->  ps )
) )
73, 6bitri 249 . 2  |-  ( ( ( ps  \/  -.  ph )  \/  -.  ( ps 
<-> 
ph ) )  <->  ( ( -.  ph  \/  ps )  \/  -.  ( ph  <->  ps )
) )
81, 7sylib 196 1  |-  ( th 
->  ( ( -.  ph  \/  ps )  \/  -.  ( ph  <->  ps ) ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 184    \/ 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:  tsxo4  29119  mpt2bi123f  29143  mptbi12f  29147  ac6s6  29152
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