Theorem mainerim

Description: Every equivalence relation implies equivalent coelements. (Contributed by Peter Mazsa, 20-Oct-2021)

	Ref	Expression
Assertion	mainerim	⊢ ( 𝑅 ErALTV 𝐴 → CoElEqvRel 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		mainer2	⊢ ( 𝑅 ErALTV 𝐴 → ( CoElEqvRel 𝐴 ∧ ¬ ∅ ∈ 𝐴 ) )
2	1	simpld	⊢ ( 𝑅 ErALTV 𝐴 → CoElEqvRel 𝐴 )