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Metamath Proof Explorer

Theorem sneqbg

Description: Two singletons of sets are equal iff their elements are equal. (Contributed by Scott Fenton, 16-Apr-2012)

Ref Expression
Assertion sneqbg ⊢ A ∈ V → A = B ↔ A = B

Proof

Step Hyp Ref Expression
1 sneqrg ⊢ A ∈ V → A = B → A = B
2 sneq ⊢ A = B → A = B
3 1 2 impbid1 ⊢ A ∈ V → A = B ↔ A = B