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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

Proof

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