Theorem inn0

Description: A nonempty intersection. (Contributed by Glauco Siliprandi, 24-Dec-2020)

	Ref	Expression
Assertion	inn0	$$⊢A\cap B\ne \varnothing \leftrightarrow \exists x\in Ax\in B$$

Proof

Step	Hyp	Ref	Expression
1		nfcv	$$⊢\underset{\_}{Ⅎ}xA$$
2		nfcv	$$⊢\underset{\_}{Ⅎ}xB$$
3	1 2	inn0f	$$⊢A\cap B\ne \varnothing \leftrightarrow \exists x\in Ax\in B$$