DefSubclass (3.06, Definition): Subclass relation

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

Formula Display:
Proof Trees:

DefSubclass (3.06) — Subclass relation

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

Num Entity Database Record (Vertical Field Table)
3.06
Title Subclass relation #DefSubclass #label-subclass-relation
Classification Definition
Formula
0\(\href{../symbols/delimiters-brackets.html}{(} \href{../symbols/forall-binder.html}{\forall} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{X} \href{../symbols/typing-colon.html}{:} \href{../symbols/class-type.html}{\mathsf{Class}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/forall-binder.html}{\forall} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{Y} \href{../symbols/typing-colon.html}{:} \href{../symbols/class-type.html}{\mathsf{Class}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{X} \href{../symbols/sub-pred.html}{\subseteq} \href{../symbols/variables.html}{Y} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/iff-conn.html}{\longleftrightarrow} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/forall-binder.html}{\forall} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{a} \href{../symbols/typing-colon.html}{:} \href{../symbols/class-type.html}{\mathsf{Class}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{a} \href{../symbols/in-pred.html}{\in} \href{../symbols/variables.html}{X} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/impl-conn.html}{\rightarrow} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{a} \href{../symbols/in-pred.html}{\in} \href{../symbols/variables.html}{Y} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \)
SML Kernel AST PSubDef_prf
Scheme of Types 0(∀([X@Variable]:[Class@Type])∀([Y@Variable]:[Class@Type])(([X@Class.Expression]⊆[Y@Class.Expression])⟷(∀([a@Variable]:[Class@Type])(([a@Class.Expression]∈[X@Class.Expression])→([a@Class.Expression]∈[Y@Class.Expression])))))
Verification Definitional (Kernel AST) · Standalone Entry (DefSubclass) → · (3.06) · #DefSubclass