Metamath Proof Explorer


Theorem bj-eu3f

Description: Version of eu3v where the disjoint variable condition is replaced with a nonfreeness hypothesis. This is a "backup" of a theorem that used to be in the main part with label "eu3" and was deprecated in favor of eu3v . (Contributed by NM, 8-Jul-1994) (Proof shortened by BJ, 31-May-2019)

Ref Expression
Hypothesis bj-eu3f.1 y φ
Assertion bj-eu3f ∃! x φ x φ y x φ x = y

Proof

Step Hyp Ref Expression
1 bj-eu3f.1 y φ
2 df-eu ∃! x φ x φ * x φ
3 1 mof * x φ y x φ x = y
4 3 anbi2i x φ * x φ x φ y x φ x = y
5 2 4 bitri ∃! x φ x φ y x φ x = y