Right Operation is Anticommutative
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Theorem
The right operation is anticommutative:
- $\forall x, y: x \rightarrow y = y \rightarrow x \iff x = y$
Proof
Immediate from the definition of the right operation.
$\blacksquare$
Also see
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text I$: Algebraic Structures: $\S 2$: Compositions: Exercise $2.17 \ \text{(a)}$