Prove that a is in the subset b if p(a) is in the subset p(b)

Show that if p(a) ⊂ p(b) then a ⊂ b. 

I will assume p() means power set. 

proof: let x∈a, then {x} ∈ p(a) and so by hypothesis {x} ∈ p(b). However {x} could not be in p(b) unless x∈b. This shows that each element of a is an element of b and hence a ⊂ b.

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