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 → MembPart 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		partimcomember	⊢ ( 𝑅 Part 𝐴 → CoMembEr 𝐴 )
2		mpet	⊢ ( MembPart 𝐴 ↔ CoMembEr 𝐴 )
3	1 2	sylibr	⊢ ( 𝑅 Part 𝐴 → MembPart 𝐴 )