Theorem issetssr

Description: Two ways of expressing set existence. (Contributed by Peter Mazsa, 1-Aug-2019)

	Ref	Expression
Assertion	issetssr	⊢ ( 𝐴 ∈ V ↔ 𝐴 S 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		brssrid	⊢ ( 𝐴 ∈ V → 𝐴 S 𝐴 )
2		relssr	⊢ Rel S
3	2	brrelex1i	⊢ ( 𝐴 S 𝐴 → 𝐴 ∈ V )
4	1 3	impbii	⊢ ( 𝐴 ∈ V ↔ 𝐴 S 𝐴 )