Metamath Proof Explorer


Theorem alimdv

Description: Deduction form of Theorem 19.20 of Margaris p. 90, see alim . See alimdh and alimd for versions without a distinct variable condition. (Contributed by NM, 3-Apr-1994)

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

Proof

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