Theorem bj-dfbi4

Description: Alternate definition of the biconditional. (Contributed by BJ, 4-Oct-2019)

	Ref	Expression
Assertion	bj-dfbi4	|- ( ( ph <-> ps ) <-> ( ( ph /\ ps ) \/ -. ( ph \/ ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		dfbi3	|- ( ( ph <-> ps ) <-> ( ( ph /\ ps ) \/ ( -. ph /\ -. ps ) ) )
2		pm4.56	|- ( ( -. ph /\ -. ps ) <-> -. ( ph \/ ps ) )
3	2	orbi2i	|- ( ( ( ph /\ ps ) \/ ( -. ph /\ -. ps ) ) <-> ( ( ph /\ ps ) \/ -. ( ph \/ ps ) ) )
4	1 3	bitri	|- ( ( ph <-> ps ) <-> ( ( ph /\ ps ) \/ -. ( ph \/ ps ) ) )