Metamath Proof Explorer


Theorem eubii

Description: Introduce unique existential quantifier to both sides of an equivalence. (Contributed by NM, 9-Jul-1994) (Revised by Mario Carneiro, 6-Oct-2016)

Ref Expression
Hypothesis eubii.1
|- ( ph <-> ps )
Assertion eubii
|- ( E! x ph <-> E! x ps )

Proof

Step Hyp Ref Expression
1 eubii.1
 |-  ( ph <-> ps )
2 eubi
 |-  ( A. x ( ph <-> ps ) -> ( E! x ph <-> E! x ps ) )
3 2 1 mpg
 |-  ( E! x ph <-> E! x ps )