Metamath Proof Explorer


Theorem mobii

Description: Formula-building rule for the at-most-one quantifier (inference form). (Contributed by NM, 9-Mar-1995) (Revised by Mario Carneiro, 17-Oct-2016)

Ref Expression
Hypothesis mobii.1
|- ( ps <-> ch )
Assertion mobii
|- ( E* x ps <-> E* x ch )

Proof

Step Hyp Ref Expression
1 mobii.1
 |-  ( ps <-> ch )
2 mobi
 |-  ( A. x ( ps <-> ch ) -> ( E* x ps <-> E* x ch ) )
3 2 1 mpg
 |-  ( E* x ps <-> E* x ch )