Theorem ts3or1

Description: A Tseitin axiom for triple logical disjunction, in deduction form. (Contributed by Giovanni Mascellani, 25-Mar-2018)

	Ref	Expression
Assertion	ts3or1	|- ( th -> ( ( ( ph \/ ps ) \/ ch ) \/ -. ( ph \/ ps \/ ch ) ) )

Proof

Step	Hyp	Ref	Expression
1		exmidd	|- ( th -> ( ( ( ph \/ ps ) \/ ch ) \/ -. ( ( ph \/ ps ) \/ ch ) ) )
2		df-3or	|- ( ( ph \/ ps \/ ch ) <-> ( ( ph \/ ps ) \/ ch ) )
3	2	notbii	|- ( -. ( ph \/ ps \/ ch ) <-> -. ( ( ph \/ ps ) \/ ch ) )
4	3	orbi2i	|- ( ( ( ( ph \/ ps ) \/ ch ) \/ -. ( ph \/ ps \/ ch ) ) <-> ( ( ( ph \/ ps ) \/ ch ) \/ -. ( ( ph \/ ps ) \/ ch ) ) )
5	1 4	sylibr	|- ( th -> ( ( ( ph \/ ps ) \/ ch ) \/ -. ( ph \/ ps \/ ch ) ) )