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 ∈ V
Assertion	epini	⊢ ( ◡ E “ { 𝐴 } ) = 𝐴

Proof

Step	Hyp	Ref	Expression
1		epini.1	⊢ 𝐴 ∈ V
2		epin	⊢ ( 𝐴 ∈ V → ( ◡ E “ { 𝐴 } ) = 𝐴 )
3	1 2	ax-mp	⊢ ( ◡ E “ { 𝐴 } ) = 𝐴