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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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