Explosion Law or Ex Falso Quodlibet

In this paper, we create a logical system that is exactly the same as Classical Logic apart from the fact that, when we have a material implication, antecedent false and consequent true or antecedent false and consequent false do not result in true. This is thought of because of an argument presented by Doctor Corcoran, which seems to convince us. The intentions are realistically ambitious: We would like to replace Classical Logic with Classical Logic', that is, simply start using these new rules from day to night in place of the current rules. We will study coherence and consistency. We will also study soundness and completeness, Priest's style. The methods we use are virtual search, analytical tools, synthetic tools, and creative, lose, or nonstandard inference.