Metamath Proof Explorer

Theorem eu3v

Description: An alternate way to express existential uniqueness. (Contributed by NM, 8-Jul-1994) Replace a nonfreeness hypothesis with a disjoint variable condition on ph , y to reduce axiom usage. (Revised by Wolf Lammen, 29-May-2019)

Ref Expression
Assertion eu3v ∃! x φ x φ y x φ x = y


Step Hyp Ref Expression
1 df-eu ∃! x φ x φ * x φ
2 df-mo * x φ y x φ x = y
3 2 anbi2i x φ * x φ x φ y x φ x = y
4 1 3 bitri ∃! x φ x φ y x φ x = y