EQ Axioms and Advice

(1) Axiom: Associativity of \(\equiv\): p \(\equiv\) (q \(\equiv\) r) \( \hspace{0.2 cm} \equiv \hspace{0.2 cm} \) (p \(\equiv\) q ) \(\equiv\) r

(2) Axiom: Symmetry of \(\equiv\): p \(\equiv\) q \( \hspace{0.2 cm} \equiv \hspace{0.2 cm} \) q \(\equiv\) p

(3) Axiom: Identity of \(\equiv\): true \(\equiv\) q \(\equiv \) q