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Theorem tsxo2 32293
Description: A Tseitin axiom for logical exclusive disjunction, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018.)
Assertion
Ref Expression
tsxo2  |-  ( th 
->  ( ( ph  \/  ps )  \/  -.  ( ph  \/_  ps )
) )

Proof of Theorem tsxo2
StepHypRef Expression
1 tsbi2 32289 . 2  |-  ( th 
->  ( ( ph  \/  ps )  \/  ( ph 
<->  ps ) ) )
2 xnor 1402 . . 3  |-  ( (
ph 
<->  ps )  <->  -.  ( ph  \/_  ps ) )
32orbi2i 521 . 2  |-  ( ( ( ph  \/  ps )  \/  ( ph  <->  ps ) )  <->  ( ( ph  \/  ps )  \/ 
-.  ( ph  \/_  ps ) ) )
41, 3sylib 199 1  |-  ( th 
->  ( ( ph  \/  ps )  \/  -.  ( ph  \/_  ps )
) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 187    \/ wo 369    \/_ wxo 1400
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 188  df-or 371  df-an 372  df-xor 1401
This theorem is referenced by: (None)
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