Metamath Proof Explorer


Theorem elsn2

Description: There is exactly one element in a singleton. Exercise 2 of TakeutiZaring p. 15. This variation requires only that B , rather than A , be a set. (Contributed by NM, 12-Jun-1994)

Ref Expression
Hypothesis elsn2.1 BV
Assertion elsn2 ABA=B

Proof

Step Hyp Ref Expression
1 elsn2.1 BV
2 elsn2g BVABA=B
3 1 2 ax-mp ABA=B