Theorem partimcomember

Description: Partition with general R (in addition to the member partition cf. mpet and mpet2 ) implies equivalent comembers. (Contributed by Peter Mazsa, 23-Sep-2021) (Revised by Peter Mazsa, 22-Dec-2024)

	Ref	Expression
Assertion	partimcomember	⊢ ( 𝑅 Part 𝐴 → CoMembEr 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		partim	⊢ ( 𝑅 Part 𝐴 → ≀ 𝑅 ErALTV 𝐴 )
2		mainer	⊢ ( ≀ 𝑅 ErALTV 𝐴 → CoMembEr 𝐴 )
3	1 2	syl	⊢ ( 𝑅 Part 𝐴 → CoMembEr 𝐴 )