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Metamath Proof Explorer

Theorem elsni

Description: There is at most one element in a singleton. (Contributed by NM, 5-Jun-1994)

Ref Expression
Assertion elsni 
|- ( A e. { B } -> A = B )

Proof

Step Hyp Ref Expression
1 elsng 
 |-  ( A e. { B } -> ( A e. { B } <-> A = B ) )
2 1 ibi 
 |-  ( A e. { B } -> A = B )