Theorem bj-dfbi5

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

	Ref	Expression
Assertion	bj-dfbi5	|- ( ( ph <-> ps ) <-> ( ( ph \/ ps ) -> ( ph /\ ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		orcom	|- ( ( ( ph /\ ps ) \/ -. ( ph \/ ps ) ) <-> ( -. ( ph \/ ps ) \/ ( ph /\ ps ) ) )
2		bj-dfbi4	|- ( ( ph <-> ps ) <-> ( ( ph /\ ps ) \/ -. ( ph \/ ps ) ) )
3		imor	|- ( ( ( ph \/ ps ) -> ( ph /\ ps ) ) <-> ( -. ( ph \/ ps ) \/ ( ph /\ ps ) ) )
4	1 2 3	3bitr4i	|- ( ( ph <-> ps ) <-> ( ( ph \/ ps ) -> ( ph /\ ps ) ) )