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Metamath Proof Explorer

Theorem brparts

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

		Ref	Expression
	Assertion	brparts	$⊢ A \in V \to (R Parts A \leftrightarrow (R \in Disjs \land R DomainQss A))$

Step	Hyp	Ref	Expression
1		df-parts	$⊢ Parts = {DomainQss ↾}_{Disjs}$
2	1	eqres	$⊢ A \in V \to (R Parts A \leftrightarrow (R \in Disjs \land R DomainQss A))$