Metamath Proof Explorer


Theorem eueqi

Description: There exists a unique set equal to a given set. Inference associated with euequ . See euequ in the case of a setvar. (Contributed by NM, 5-Apr-1995)

Ref Expression
Hypothesis eueqi.1 ⊢ A ∈ V
Assertion eueqi ⊢ ∃! x x = A

Proof

Step Hyp Ref Expression
1 eueqi.1 ⊢ A ∈ V
2 eueq ⊢ A ∈ V ↔ ∃! x x = A
3 1 2 mpbi ⊢ ∃! x x = A