Equality of Mappings

Theorem
Two mappings $f_1: S_1 \to T_1, f_2: S_2 \to T_2$ are equal :


 * $(1): \quad S_1 = S_2$
 * $(2): \quad T_1 = T_2$
 * $(3): \quad \forall x \in S_1: \map {f_1} x = \map {f_2} x$

Proof
This follows directly from Equality of Relations.