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Metamath Proof Explorer

Theorem issetssr

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

		Ref	Expression
	Assertion	issetssr	$⊢ A \in V \leftrightarrow A S A$

Step	Hyp	Ref	Expression
1		brssrid	$⊢ A \in V \to A S A$
2		relssr	$⊢ Rel S$
3	2	brrelex1i	$⊢ A S A \to A \in V$
4	1 3	impbii	$⊢ A \in V \leftrightarrow A S A$