Metamath Proof Explorer

Theorem exmoeub

Description: Existence implies that uniqueness is equivalent to unique existence. (Contributed by NM, 5-Apr-2004)

Ref Expression
Assertion exmoeub 
|- ( E. x ph -> ( E* x ph <-> E! x ph ) )

Proof

Step Hyp Ref Expression
1 df-eu 
 |-  ( E! x ph <-> ( E. x ph /\ E* x ph ) )
2 1 baibr 
 |-  ( E. x ph -> ( E* x ph <-> E! x ph ) )