Final answer:
The property of equality demonstrated in the given expression is the Addition Property of Equality, which states that adding the same number to both sides of an equation does not change the equality.
Step-by-step explanation:
The property of equality demonstrated in the given expression is the Addition Property of Equality.
According to this property, if we add the same number to both sides of an equation, the equality is not changed. In the given expression x + 78 = w - 23 + 78, by adding 78 to both sides, we maintain the equality between the two sides.