Metamath Proof Explorer


Theorem reu5

Description: Restricted uniqueness in terms of "at most one". (Contributed by NM, 23-May-1999) (Revised by NM, 16-Jun-2017)

Ref Expression
Assertion reu5 ∃!xAφxAφ*xAφ

Proof

Step Hyp Ref Expression
1 df-eu ∃!xxAφxxAφ*xxAφ
2 df-reu ∃!xAφ∃!xxAφ
3 df-rex xAφxxAφ
4 df-rmo *xAφ*xxAφ
5 3 4 anbi12i xAφ*xAφxxAφ*xxAφ
6 1 2 5 3bitr4i ∃!xAφxAφ*xAφ