Metamath Proof Explorer

Theorem dfdisjALTV2

Description: Alternate definition of the disjoint relation predicate, cf. dffunALTV2 . (Contributed by Peter Mazsa, 27-Jul-2021)

Ref Expression
Assertion dfdisjALTV2 
|- ( Disj R <-> ( ,~ `' R C_ _I /\ Rel R ) )

Proof

Step Hyp Ref Expression
1 df-disjALTV 
 |-  ( Disj R <-> ( CnvRefRel ,~ `' R /\ Rel R ) )
2 cnvrefrelcoss2 
 |-  ( CnvRefRel ,~ `' R <-> ,~ `' R C_ _I )
3 2 anbi1i 
 |-  ( ( CnvRefRel ,~ `' R /\ Rel R ) <-> ( ,~ `' R C_ _I /\ Rel R ) )
4 1 3 bitri 
 |-  ( Disj R <-> ( ,~ `' R C_ _I /\ Rel R ) )