DefUnorderedPair (3.49, Definition): Unordered pair

Standalone kernel entity record from 3. Set/Class-Theoretic Foundations (3.01–3.78) — View in Complete Entity Database (#DefUnorderedPair) →

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DefUnorderedPair (3.49) — Unordered pair

Morse-Kelley / Von Neumann-Bernays-Gödel class comprehension, sethood, ordinals, Dunaev pairs, cardinals, universes, and reflection.

Num Entity Database Record (Vertical Field Table)
3.49
Title Unordered pair #DefUnorderedPair #label-unordered-pair
Classification Definition
Formula
0\(\href{../symbols/delimiters-brackets.html}{(} \href{../symbols/forall-binder.html}{\forall} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{a} \href{../symbols/typing-colon.html}{:} \href{../symbols/class-type.html}{\mathsf{Class}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/forall-binder.html}{\forall} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{b} \href{../symbols/typing-colon.html}{:} \href{../symbols/class-type.html}{\mathsf{Class}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/upair-op.html}{\{} \href{../symbols/variables.html}{a} \href{../symbols/comma-delim.html}{,} \href{../symbols/variables.html}{b} \href{../symbols/upair-op.html}{\}} \href{../symbols/eq-pred.html}{=} \href{../symbols/class-comprehension.html}{\{} \href{../symbols/variables.html}{x} \href{../symbols/class-comprehension.html}{ \mid } \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{x} \href{../symbols/eq-pred.html}{=} \href{../symbols/variables.html}{a} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/or-conn.html}{\lor} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{x} \href{../symbols/eq-pred.html}{=} \href{../symbols/variables.html}{b} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/class-comprehension.html}{\}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \)
SML Kernel AST CpUPair
Scheme of Types 0(∀([a@Variable]:[Class@Type])∀([b@Variable]:[Class@Type])({[a@Class.Expression],[b@Class.Expression]}={[x@Class.Expression]|([x@Class.Expression]=[a@Class.Expression])∨([x@Class.Expression]=[b@Class.Expression])}))
Verification Definitional (Kernel AST) · Standalone Entry (DefUnorderedPair) → · (3.49) · #DefUnorderedPair