Linked from

The 11 pages that link to Axiom of extensionality, each with the reason it gives.

• Zermelo–Fraenkel set theoryRelated: It fixes when two sets count as the same object.

• Ordered pairRelated: It helps establish that the Kuratowski encoding obeys the intended equality rule.

• Choice functionRelated: Its inputs are sets, whose identity depends only on their elements.

• ElementRelated: It makes a set depend on its elements, not on how it is described.

• Axiom of FoundationRelated: Extensionality and Foundation jointly govern the identity and membership structure of sets.

• Membership relationRelated: It makes a set fully determined by which membership claims hold.

• Axiom of Power SetRelated: It ensures that a set containing exactly the subsets is unique.

• New FoundationsRelated: New Foundations retains extensionality alongside its restricted comprehension scheme.

• Axiom of regularityRelated: Together with regularity, it supports familiar structural claims about sets and membership.

• Axiom of Empty SetRelated: It makes the empty set unique once existence is established.

• Mostowski collapse lemmaRelated: It explains why membership on sets distinguishes objects by their predecessors.