Theorem ts3or3

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

	Ref	Expression
Assertion	ts3or3	|- ( th -> ( -. ch \/ ( ph \/ ps \/ ch ) ) )

Proof

Step	Hyp	Ref	Expression
1		tsor3	|- ( th -> ( -. ch \/ ( ( ph \/ ps ) \/ ch ) ) )
2		df-3or	|- ( ( ph \/ ps \/ ch ) <-> ( ( ph \/ ps ) \/ ch ) )
3	2	orbi2i	|- ( ( -. ch \/ ( ph \/ ps \/ ch ) ) <-> ( -. ch \/ ( ( ph \/ ps ) \/ ch ) ) )
4	1 3	sylibr	|- ( th -> ( -. ch \/ ( ph \/ ps \/ ch ) ) )