 This time the target inference, to be declared invalid, is the one we above call ex falso quodlibet, abbreviated (EFQ):  \[ {\rm If} \ \Gamma_1 \vdash \Theta \ {\rm and} \ \Gamma_2 \vdash \neg\Theta \ {\rm then} \ \Gamma_1, \Gamma_2 \vdash \Psi \]  We can focus attention one kind of instance of this:  \[ \Phi, \neg\Phi \vdash \Psi, \]  sometimes colorfully called “explosion”. It says that anything at all follows from a contradiction.