Axiom of Choice (Premise) Use this premise to introduce the Axiom of Choice at the beginning of a proof. Where: f = family of sets i = index set f(j) = jth element of f c(j) = choice from the jth element of f 1 ALL(f):ALL(i):[Set(f) & Set(i) & EXIST(a):ai & ALL(a):[a
f => Set(a) & EXIST(b):b
a] & ALL(a):[a
i => f(a)
f] & ALL(a):[a
f => EXIST(b):[b
i & a=f(b)]] => EXIST(c):ALL(a):[a
i => c(a)
f(a)]] Premise