Theorem 1cosscnvepresex

Description: Sufficient condition for a restricted converse epsilon coset to be a set. (Contributed by Peter Mazsa, 24-Sep-2021)

	Ref	Expression
Assertion	1cosscnvepresex	⊢ ( 𝐴 ∈ 𝑉 → ≀ ( ◡ E ↾ 𝐴 ) ∈ V )

Proof

Step	Hyp	Ref	Expression
1		cnvepresex	⊢ ( 𝐴 ∈ 𝑉 → ( ◡ E ↾ 𝐴 ) ∈ V )
2		cossex	⊢ ( ( ◡ E ↾ 𝐴 ) ∈ V → ≀ ( ◡ E ↾ 𝐴 ) ∈ V )
3	1 2	syl	⊢ ( 𝐴 ∈ 𝑉 → ≀ ( ◡ E ↾ 𝐴 ) ∈ V )