Metamath Proof Explorer


Theorem ralrimdv

Description: Inference from Theorem 19.21 of Margaris p. 90. (Restricted quantifier version.) (Contributed by NM, 27-May-1998) Reduce dependencies on axioms. (Revised by Wolf Lammen, 28-Dec-2019)

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

Proof

Step Hyp Ref Expression
1 ralrimdv.1
 |-  ( ph -> ( ps -> ( x e. A -> ch ) ) )
2 1 imp
 |-  ( ( ph /\ ps ) -> ( x e. A -> ch ) )
3 2 ralrimiv
 |-  ( ( ph /\ ps ) -> A. x e. A ch )
4 3 ex
 |-  ( ph -> ( ps -> A. x e. A ch ) )