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 e. _V
Assertion	epini	|- ( `' _E " { A } ) = A

Proof

Step	Hyp	Ref	Expression
1		epini.1	|- A e. _V
2		epin	|- ( A e. _V -> ( `' _E " { A } ) = A )
3	1 2	ax-mp	|- ( `' _E " { A } ) = A