Subset Relation is Reflexive

Theorem

Let $C$ be a class.

The subset relation $\subseteq$ on $C$ is a reflexive relation on $C$.

$\ds \forall x \in C: \, $

$\ds x$

$\subseteq$

$\ds x$

$\ds \leadsto \ \ $

$\ds \forall x \in C: \, $

$\ds \tuple {x, x}$

$\in$

$\ds \subseteq$

So $\subseteq$ is reflexive.

$\blacksquare$

2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $4$: Superinduction, Well Ordering and Choice: Part $\text I$ -- Superinduction and Well Ordering: $\S 1$ Introduction to well ordering