Theorem snidg

Description: A set is a member of its singleton. Part of Theorem 7.6 of Quine p. 49. (Contributed by NM, 28-Oct-2003)

	Ref	Expression
Assertion	snidg	⊢ ( 𝐴 ∈ 𝑉 → 𝐴 ∈ { 𝐴 } )

Proof

Step	Hyp	Ref	Expression
1		eqid	⊢ 𝐴 = 𝐴
2		elsng	⊢ ( 𝐴 ∈ 𝑉 → ( 𝐴 ∈ { 𝐴 } ↔ 𝐴 = 𝐴 ) )
3	1 2	mpbiri	⊢ ( 𝐴 ∈ 𝑉 → 𝐴 ∈ { 𝐴 } )