Epsilon-induction
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In mathematics, ∈-induction (epsilon-induction) is a variant of transfinite induction, which can be used in set theory to prove that all sets satisfy a given property P(x). If the truth of the property for x follows from its truth for all elements of x, for every set x, then the property is true of all sets. In symbols:
This principle is equivalent to the axiom of regularity. It can be converted into a transfinite induction on the rank of the set x.
The name is most often pronounced "epsilon-induction", because the set membership symbol 
historically developed from the Greek letter 
.
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