Metamath Proof Explorer


Theorem tsxo3

Description: A Tseitin axiom for logical exclusive disjunction, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018)

Ref Expression
Assertion tsxo3
|- ( th -> ( ( ph \/ -. ps ) \/ ( ph \/_ ps ) ) )

Proof

Step Hyp Ref Expression
1 tsbi3
 |-  ( th -> ( ( ph \/ -. ps ) \/ -. ( ph <-> ps ) ) )
2 df-xor
 |-  ( ( ph \/_ ps ) <-> -. ( ph <-> ps ) )
3 2 bicomi
 |-  ( -. ( ph <-> ps ) <-> ( ph \/_ ps ) )
4 3 orbi2i
 |-  ( ( ( ph \/ -. ps ) \/ -. ( ph <-> ps ) ) <-> ( ( ph \/ -. ps ) \/ ( ph \/_ ps ) ) )
5 1 4 sylib
 |-  ( th -> ( ( ph \/ -. ps ) \/ ( ph \/_ ps ) ) )