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Metamath Proof Explorer

Theorem epini

Description: Any set is equal to its preimage under the converse membership relation. (Contributed by Mario Carneiro, 9-Mar-2013)

		Ref	Expression
	Hypothesis	epini.1	$⊢ A \in V$
	Assertion	epini	$⊢ E^{-1} [\{A\}] = A$

Step	Hyp	Ref	Expression
1		epini.1	$⊢ A \in V$
2		epin	$⊢ A \in V \to E^{-1} [\{A\}] = A$
3	1 2	ax-mp	$⊢ E^{-1} [\{A\}] = A$