Let $L$ be the set of equivalence classes of statement forms $[\phi]$.
The partial order defined on these classes is the natural partial order of Boolean algebras, i.e., $[\phi]\leq [\psi]$ if and only if $(\phi \Rightarrow \psi)$ is true.
If we denote the set of all equivalence classes of statement forms by $C$, prove that $(C, \leq)$ is a lattice.
I know that the given structure is a lattice iff every two elements have a supremum and an infimum and I feel that the infimum is $[A \wedge \neg A]$, but the supremum I do not know. Could anyone help me?