Metamath Proof Explorer


Theorem eubrv

Description: If there is a unique set which is related to a class, then the class must be a set. (Contributed by AV, 25-Aug-2022)

Ref Expression
Assertion eubrv ⊢ ∃! b A R b → A ∈ V

Proof

Step Hyp Ref Expression
1 brprcneu ⊢ ¬ A ∈ V → ¬ ∃! b A R b
2 1 con4i ⊢ ∃! b A R b → A ∈ V