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math_proof
i have couple proof problems with a field of given axioms, please help
axioms: i) ∀a,b,c∈F, (a+b)+c=a+(b+c) ii) ∀a∈F, 0+a=a iii) ∀a∈F, ∃a ̃∈F, a ̃+a=0 iv) ∀a,b∈F, a+b=b+a v) ∀a,b,c ∈ F, (ab)c = a(bc) vi) ∀a∈F, 1a=a vii) ∀a∈F, ∼(a=0)⇒∃a′ ∈F,a′a=1 viii) ∀a, b ∈ F, ab = ba ix) ∀a,b,c∈F, (a+b)c=ac+bc problem 3) If 0 = 1, then ∀a ∈ F,a = 0. (5) Ifa∈F and x∈F is an element such that x+a=0,then x =a' (6) ∀a∈A,a''=a (7) ∀a∈1'a=a' (a' inverse)