please use ONLY inference rules for Propositional Logic plus the basic QL inference rules plus Universal Introduction

Write the answer in the format of the above rules given and that is how it should be written out as you can also see in some of the steps given in the problem.

I will give a thumbs up for a correct answer that follows the instructions given and answers the problem thoroughly and completely!!

Inference Rules for F PR/AS R i. A PR/AS i. A D). A Ri & Intro & Elim i. A j.B Dk. ALB i AAB 1. A/B & Elimi & Intro 1,3 VIntro VElim 1. A/B AVB VIntro i. AVB |j. B/A 1. A/B VElimi, Intro Elim LA AS -A AS j.B k.-B 3. B k. -B DA D 1. - Intro i-k Elimik Intro Elim i. A AS i. A B |j. A k. B Elim: i, j 1.B KAB + Intro: i- Intro #Elim i. A AS AB j. A/B Dk. B/A ok Elimij 3.B k. B AS 2. A m AB Intro i-jk-1 Intro Quantifier and Identity Inference Rules i. A(m) 3 Elim i. 3xA(X) j. 3xM(X) Intro: i .j. mA(m) : D k. B Dl. B Elim: i, G, k) VIntro VElim m i. VXA(x) 1. A(m) VElim: i j. A(m) D 1. V AC VIntro: i, Intro =Intro =Elim Di m = m i. A(m) j. m = n Dk. A(n/m) =Elim: i, (axFx ayHy) - vx(Fx ayHy) 1 ExFx>EyHy : PR HN 3 Ax(Fx>EyHy)