This statement is said to be contraposed to the original and is logically equivalent to it.

To prove that contrapositives are logically equivalent, we need to understand when material implication is true or false.

Each definition is producing a logically equivalent formula that can be used for substitution or replacement.

Complement the result, the result is logically equivalent to what you started with.

By "logically equivalent" is meant that the two expressions have the same simplification.

Within the context of a logical proof, logically equivalent expressions may replace each other.

Formulas, built from terms in the usual way, can be equated if they are logically equivalent.

Notice that when is commutative, then the three above conditions are logically equivalent.

For some disturbed souls, such a loss was logically equivalent to the death of the beloved.

For instance, the formula is logically equivalent to .