DefBigDomain (3.21, Definition): Domain (includes arguments with proper class values)

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

Formula Display:
Proof Trees:

DefBigDomain (3.21) — Domain (includes arguments with proper class values)

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

Num Entity Database Record (Vertical Field Table)
3.21
Title Domain (includes arguments with proper class values) #DefBigDomain #label-domain-includes-arguments-with-proper-class-values
Classification Definition
Formula
0\(\href{../symbols/delimiters-brackets.html}{(} \href{../symbols/forall-binder.html}{\forall} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{F} \href{../symbols/typing-colon.html}{:} \href{../symbols/class-type.html}{\mathsf{Class}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/dom-op.html}{\mathrm{Dom}} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{F} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/eq-pred.html}{=} \href{../symbols/class-comprehension.html}{\{} \href{../symbols/variables.html}{x} \href{../symbols/class-comprehension.html}{ \mid } \href{../symbols/exists-binder.html}{\exists} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{b} \href{../symbols/typing-colon.html}{:} \href{../symbols/class-type.html}{\mathsf{Class}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{x} \href{../symbols/comma-delim.html}{,} \href{../symbols/variables.html}{b} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/in-pred.html}{\in} \href{../symbols/variables.html}{F} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/class-comprehension.html}{\}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \)
SML Kernel AST CpDom
Scheme of Types 0(∀([F@Variable]:[Class@Type])(Dom([F@Class.Expression])={[x@Class.Expression]|∃([b@Variable]:[Class@Type])(([x@Class.Expression],[b@Class.Expression])∈[F@Class.Expression])}))
Verification Definitional (Kernel AST) · Standalone Entry (DefBigDomain) → · (3.21) · #DefBigDomain