Metamath Proof Explorer


Theorem eximdv

Description: Deduction form of Theorem 19.22 of Margaris p. 90, see exim . See eximdh and eximd for versions without a distinct variable condition. (Contributed by NM, 27-Apr-1994)

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

Proof

Step Hyp Ref Expression
1 alimdv.1
 |-  ( ph -> ( ps -> ch ) )
2 ax-5
 |-  ( ph -> A. x ph )
3 2 1 eximdh
 |-  ( ph -> ( E. x ps -> E. x ch ) )