The Law of Noncontradiction

From Logic

The Law of Noncontradiction can be proven using Propositional Logic:

Proof (by reductio):

1) (A & ~A) [Proposition] 2) A [Conjunction elimination from 1] 3) ~A [Conjunction elimination from 1] 4) ~(A & ~A) [Reductio, 1 - 3]

QED