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we have the following formal proof:

i) \(\displaystyle \forall x[\forall y(xy=y)\Longrightarrow x=1]\)........................................theoren in real Nos

2)\(\displaystyle \forall y(xy=y)\Longrightarrow x=1\).......................1,U.E ,x=x

3) \(\displaystyle (x0=0)\Longrightarrow x=1\)....................... 2,U.E ,y=0

4)\(\displaystyle \forall A[A.0=0]\).....................................Theorem in Real Nos

5) )\(\displaystyle [x.0=0]\).....................................4,U.E, A=x

6) x=1.........................................3,5 M.Ponens

7) )\(\displaystyle \forall A[A=1]\)..................................... 6,U.I

U.E=Universal Elimination

U.I = Universal Introduction

I am afraid to say i find no mistake

i) \(\displaystyle \forall x[\forall y(xy=y)\Longrightarrow x=1]\)........................................theoren in real Nos

2)\(\displaystyle \forall y(xy=y)\Longrightarrow x=1\).......................1,U.E ,x=x

3) \(\displaystyle (x0=0)\Longrightarrow x=1\)....................... 2,U.E ,y=0

4)\(\displaystyle \forall A[A.0=0]\).....................................Theorem in Real Nos

5) )\(\displaystyle [x.0=0]\).....................................4,U.E, A=x

6) x=1.........................................3,5 M.Ponens

7) )\(\displaystyle \forall A[A=1]\)..................................... 6,U.I

U.E=Universal Elimination

U.I = Universal Introduction

I am afraid to say i find no mistake

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