Proposition 2

Tag 056U, permanent. Cite it as [Bourbaki, Tag 056U].

Algebra, chapter I, § 2. Identity element; cancellable elements; invertible elements

The set of cancellable (resp. left cancellable, resp. right cancellable) elements of an associative magma is a submagma.

If $\gamma_x$ and $\gamma_y$ are injective so is $\gamma_{x \mathsf{T} y} = \gamma_x \circ \gamma_y$ (Proposition 1). Similarly for $\delta_{x \mathsf{T} y}$ .

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Proposition 6, § 2
Proposition 1 (« addition of inequalities »), § 1

Cites

Proposition 1