ThmOrdinalsCardinal (3.66, Theorem): On is a cardinal class

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

Formula Display:
Proof Trees:

ThmOrdinalsCardinal (3.66) — On is a cardinal class

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

Num Entity Database Record (Vertical Field Table)
3.66
Title On is a cardinal class #ThmOrdinalsCardinal #label-on-is-a-cardinal-class
Classification Theorem
Formula
0Card(On)
0\(\href{../symbols/card-pred.html}{\mathrm{Card}} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/on-const.html}{\mathbf{On}} \href{../symbols/delimiters-brackets.html}{)} \)
SML Kernel AST TpCard
Scheme of Types 0Card(On)
Verification Verified (Kernel) · Standalone Entry (ThmOrdinalsCardinal) → · (3.66) · #ThmOrdinalsCardinal