Metamath Proof Explorer


Theorem brparts

Description: Binary partitions relation. (Contributed by Peter Mazsa, 23-Jul-2021)

Ref Expression
Assertion brparts Could not format assertion : No typesetting found for |- ( A e. V -> ( R Parts A <-> ( R e. Disjs /\ R DomainQss A ) ) ) with typecode |-

Proof

Step Hyp Ref Expression
1 df-parts Could not format Parts = ( DomainQss |` Disjs ) : No typesetting found for |- Parts = ( DomainQss |` Disjs ) with typecode |-
2 1 eqres Could not format ( A e. V -> ( R Parts A <-> ( R e. Disjs /\ R DomainQss A ) ) ) : No typesetting found for |- ( A e. V -> ( R Parts A <-> ( R e. Disjs /\ R DomainQss A ) ) ) with typecode |-