Theorem oibabs

Description: Absorption of disjunction into equivalence. (Contributed by NM, 6-Aug-1995) (Proof shortened by Wolf Lammen, 3-Nov-2013)

	Ref	Expression
Assertion	oibabs	|- ( ( ( ph \/ ps ) -> ( ph <-> ps ) ) <-> ( ph <-> ps ) )

Proof

Step	Hyp	Ref	Expression
1		norbi	|- ( -. ( ph \/ ps ) -> ( ph <-> ps ) )
2		id	|- ( ( ph <-> ps ) -> ( ph <-> ps ) )
3	1 2	ja	|- ( ( ( ph \/ ps ) -> ( ph <-> ps ) ) -> ( ph <-> ps ) )
4		ax-1	|- ( ( ph <-> ps ) -> ( ( ph \/ ps ) -> ( ph <-> ps ) ) )
5	3 4	impbii	|- ( ( ( ph \/ ps ) -> ( ph <-> ps ) ) <-> ( ph <-> ps ) )