Theorem ndisj

Description: Express that an intersection is not empty. (Contributed by RP, 16-Apr-2020)

	Ref	Expression
Assertion	ndisj	|- ( ( A i^i B ) =/= (/) <-> E. x ( x e. A /\ x e. B ) )

Proof

Step	Hyp	Ref	Expression
1		n0	|- ( ( A i^i B ) =/= (/) <-> E. x x e. ( A i^i B ) )
2		elin	|- ( x e. ( A i^i B ) <-> ( x e. A /\ x e. B ) )
3	2	exbii	|- ( E. x x e. ( A i^i B ) <-> E. x ( x e. A /\ x e. B ) )
4	1 3	bitri	|- ( ( A i^i B ) =/= (/) <-> E. x ( x e. A /\ x e. B ) )