Metamath Proof Explorer


Theorem eldisjs3

Description: Elementhood in the class of disjoints. (Contributed by Peter Mazsa, 5-Sep-2021)

Ref Expression
Assertion eldisjs3 R Disjs u v x u R x v R x u = v R Rels

Proof

Step Hyp Ref Expression
1 eldisjs2 R Disjs R -1 I R Rels
2 cosscnvssid3 R -1 I u v x u R x v R x u = v
3 2 anbi1i R -1 I R Rels u v x u R x v R x u = v R Rels
4 1 3 bitri R Disjs u v x u R x v R x u = v R Rels