Metamath Proof Explorer

Theorem sneqr

Description: If the singletons of two sets are equal, the two sets are equal. Part of Exercise 4 of TakeutiZaring p. 15. (Contributed by NM, 27-Aug-1993)

Ref Expression
Hypothesis sneqr.1 A V
Assertion sneqr A = B A = B


Step Hyp Ref Expression
1 sneqr.1 A V
2 sneqrg A V A = B A = B
3 1 2 ax-mp A = B A = B