Metamath Proof Explorer


Theorem moimdv

Description: The at-most-one quantifier reverses implication, deduction form. (Contributed by Thierry Arnoux, 25-Feb-2017)

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

Proof

Step Hyp Ref Expression
1 moimdv.1
 |-  ( ph -> ( ps -> ch ) )
2 1 alrimiv
 |-  ( ph -> A. x ( ps -> ch ) )
3 moim
 |-  ( A. x ( ps -> ch ) -> ( E* x ch -> E* x ps ) )
4 2 3 syl
 |-  ( ph -> ( E* x ch -> E* x ps ) )