Right Cancellable Element is Right Cancellable in Subset

Theorem
Let $\struct {S, \circ}$ be an algebraic structure.

Let $\struct {T, \circ} \subseteq \struct {S, \circ}$.

Let $x \in T$ be right cancellable in $S$.

Then $x$ is also right cancellable in $T$.

Proof
Let $x \in T$ be right cancellable in $S$.

That is:
 * $\forall a, b \in S: a \circ x = b \circ x \implies a = b$

Therefore:
 * $\forall c, d \in T: c \circ x = d \circ x \implies c = d$

Thus $x$ is right cancellable in $T$.