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Metamath Proof Explorer

Theorem mainpart

Description: Partition with general R also imply member partition. (Contributed by Peter Mazsa, 23-Sep-2021) (Revised by Peter Mazsa, 22-Dec-2024)

		Ref	Expression
	Assertion	mainpart	$⊢ R Part A \to MembPart A$

Proof

Step	Hyp	Ref	Expression
1		partimcomember	$⊢ R Part A \to CoMembEr A$
2		mpet	$⊢ MembPart A \leftrightarrow CoMembEr A$
3	1 2	sylibr	$⊢ R Part A \to MembPart A$