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