Here I show that it is true via a truth table.

\[
\begin{array}{c c c | c c | c c | c }
b & c & d & b \wedge c & ( b \wedge c ) \le d & c \Rightarrow d & b \le ( c \Rightarrow d ) & ( b \wedge c ) \le d = b \le ( c \Rightarrow d ) \\\\
\hline
\text{true} & \text{true} & \text{true} & \text{true} & \text{true} & \text{true} & \text{true} & \text{true} \\\\
\text{true} & \text{true} & \text{false} & \text{true} & \text{false} & \text{false} & \text{false} & \text{true} \\\\
\text{true} & \text{false} & \text{true} & \text{false} & \text{true} & \text{true} & \text{true} & \text{true} \\\\
\text{true} & \text{false} & \text{false} & \text{false} & \text{true} & \text{true} & \text{true} & \text{true} \\\\
\text{false} & \text{true} & \text{true} & \text{false} & \text{true} & \text{true} & \text{true} & \text{true} \\\\
\text{false} & \text{true} & \text{false} & \text{false} & \text{true} & \text{false} & \text{true} & \text{true} \\\\
\text{false} & \text{false} & \text{true} & \text{false} & \text{true} & \text{true} & \text{true} & \text{true} \\\\
\text{false} & \text{false} & \text{false} & \text{false} & \text{true} & \text{true} & \text{true} & \text{true} \\\\
\end{array}
\]

A more interesting approach would support the notion that they are equal because **Bool** is a quantale.