Theorem tsxo1

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

	Ref	Expression
Assertion	tsxo1	|- ( th -> ( ( -. ph \/ -. ps ) \/ -. ( ph \/_ ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		tsbi1	|- ( th -> ( ( -. ph \/ -. ps ) \/ ( ph <-> ps ) ) )
2		xnor	|- ( ( ph <-> ps ) <-> -. ( ph \/_ ps ) )
3	2	orbi2i	|- ( ( ( -. ph \/ -. ps ) \/ ( ph <-> ps ) ) <-> ( ( -. ph \/ -. ps ) \/ -. ( ph \/_ ps ) ) )
4	1 3	sylib	|- ( th -> ( ( -. ph \/ -. ps ) \/ -. ( ph \/_ ps ) ) )