principle of explosion or ex falso quodlibet is the observation that any argument in which the premises form an unsatisfiable set is valid. A specific example is when there is a signal premise and it is an contradiction.

Ex falso quodlibet means "from falsehood, anything [follows]" in Latin.

The phrase “and I’m the queen of England!” is often used as sarcastic comment can be seen as an informal, colloquial example of ex falso quodlibet.

Symbolic Representation

We can express the principle of explosion symbolically as the following:

Which reads as: for any statements and , if and not are both true, then it logically followed that is true.