Why if we assume p and ¬p we can prove any statememt?

Question

Every proof I find is a truth table, could somebody explain it to me intuitively?

In: 1

Answer 1

This is easily shown in classical bivalent logic.

1. p AND NOTp
2. p (1)
3. p OR q (2, ADD)
4. NOTp (1)
5. q (3,4)

You’ve just shown any statement (q) can be derived from a contradiction.