Principle of explosion
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The principle of explosion is a logical rule of inference. According to the rule, from a set of premises in which a sentence and its negation are both true (i.e., a contradiction is true), any sentence may be inferred. It is also known by its Latin name ex contradictione quodlibet, meaning from a contradiction anything follows, or ECQ for short.
Classical logic accepts the principle of explosion; but in paraconsistent logic it is rejected. It is also rejected in relevance logic, since relevance logic is based on the competing principle that the premises must be relevant to the conclusion. (All relevance logics are paraconsistent, but not all paraconsistent logics are relevant.)
Formally, the rule is stated as follows. For arbitrary sentences and :
Informally, the rule is applied thus: Suppose that one has and for premises and wishes to prove . One then may employ reductio ad absurdum, assuming to the contrary and then bringing down the premises and . This is, of course, a contradiction, meaning that may be concluded to be false, i.e., is true.
 Tacit applications
The Bible is known to contain numerous inconsistencies. Although for obvious reasons the principle of explosion is not used to draw conclusions from them, the many inconsistencies allow a Bible quote to be furnished to support just about any position imaginable, across the spectra of politics, economics, and emotions.