Metamath Proof Explorer


Theorem ralrimia

Description: Inference from Theorem 19.21 of Margaris p. 90 (restricted quantifier version). (Contributed by Glauco Siliprandi, 23-Oct-2021)

Ref Expression
Hypotheses ralrimia.1
|- F/ x ph
ralrimia.2
|- ( ( ph /\ x e. A ) -> ps )
Assertion ralrimia
|- ( ph -> A. x e. A ps )

Proof

Step Hyp Ref Expression
1 ralrimia.1
 |-  F/ x ph
2 ralrimia.2
 |-  ( ( ph /\ x e. A ) -> ps )
3 2 ex
 |-  ( ph -> ( x e. A -> ps ) )
4 1 3 ralrimi
 |-  ( ph -> A. x e. A ps )