ThmDex – An index of mathematical definitions, results, and conjectures.
Result R2767 on D467: Injective map
Identity map is an injection
Formulation 0
Let $X$ be a D11: Set such that
(i) $I : X \to Y$ is an D440: Identity map on $X$
Then $I$ is an D467: Injective map.
Subresults
▶ R301: Canonical identity map is an injection
Proofs
Proof 0
Let $X$ be a D11: Set such that
(i) $I : X \to Y$ is an D440: Identity map on $X$
For all $x, y \in X$, we have $x = I(x) = I(y) = y$. The claim follows. $\square$