Theorem tsbi4

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

	Ref	Expression
Assertion	tsbi4	|- ( th -> ( ( -. ph \/ ps ) \/ -. ( ph <-> ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		tsbi3	|- ( th -> ( ( ps \/ -. ph ) \/ -. ( ps <-> ph ) ) )
2		orcom	|- ( ( ps \/ -. ph ) <-> ( -. ph \/ ps ) )
3		bicom	|- ( ( ps <-> ph ) <-> ( ph <-> ps ) )
4	3	notbii	|- ( -. ( ps <-> ph ) <-> -. ( ph <-> ps ) )
5	2 4	orbi12i	|- ( ( ( ps \/ -. ph ) \/ -. ( ps <-> ph ) ) <-> ( ( -. ph \/ ps ) \/ -. ( ph <-> ps ) ) )
6	1 5	sylib	|- ( th -> ( ( -. ph \/ ps ) \/ -. ( ph <-> ps ) ) )