Theorem tsxo4

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

	Ref	Expression
Assertion	tsxo4	|- ( th -> ( ( -. ph \/ ps ) \/ ( ph \/_ ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		tsbi4	|- ( 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 ) ) )