Metamath Proof Explorer


Theorem ecidsn

Description: An equivalence class modulo the identity relation is a singleton. (Contributed by NM, 24-Oct-2004)

Ref Expression
Assertion ecidsn [ 𝐴 ] I = { 𝐴 }

Proof

Step Hyp Ref Expression
1 df-ec [ 𝐴 ] I = ( I “ { 𝐴 } )
2 imai ( I “ { 𝐴 } ) = { 𝐴 }
3 1 2 eqtri [ 𝐴 ] I = { 𝐴 }