Metamath Proof Explorer

Theorem inn0

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

Ref Expression
Assertion inn0 
|- ( ( A i^i B ) =/= (/) <-> E. x e. A x e. B )

Proof

Step Hyp Ref Expression
1 nfcv 
 |-  F/_ x A
2 nfcv 
 |-  F/_ x B
3 1 2 inn0f 
 |-  ( ( A i^i B ) =/= (/) <-> E. x e. A x e. B )