(related to Corollary: Commutativity of Equivalence)

- Let $L$ be a set of propositions and let $I$ be an interpretation with the valuation function $[[]]_I$.
- According to the truth table of equivalence, the valuation function $[[x\Leftrightarrow y]]_I$ does not change its value if we exchange the valuations of $[[x]]_I$ and $[[y]]_I,$
- Thus, the equivalence operation "$\Leftrightarrow$" is commutative, i.e. $x \Leftrightarrow y=y \Leftrightarrow x$.∎

**Mendelson Elliott**: "Theory and Problems of Boolean Algebra and Switching Circuits", McGraw-Hill Book Company, 1982