Metamath Proof Explorer

Theorem disj2

Description: Two ways of saying that two classes are disjoint. (Contributed by NM, 17-May-1998)

Ref Expression
Assertion disj2 
|- ( ( A i^i B ) = (/) <-> A C_ ( _V \ B ) )

Proof

Step Hyp Ref Expression
1 ssv 
 |-  A C_ _V
2 reldisj 
 |-  ( A C_ _V -> ( ( A i^i B ) = (/) <-> A C_ ( _V \ B ) ) )
3 1 2 ax-mp 
 |-  ( ( A i^i B ) = (/) <-> A C_ ( _V \ B ) )